The Voter's Paradox

An Introduction to the Theory of Social Dilemmas

By: Leon Felkins


Written November, 1994

Revised July 1, 1995


Diabolical Choices of the Individual in a Group

It is said that society is in a moral crisis. And, what is worse, it seems to be deteriorating at an ever increasing rate. We all agree that something needs to be done. Our politicians and preachers say we need to help each other more, we need to have "family values", we need to contribute to society and we need to have high moral standards. But there is a fundamental logical reason why none of this is going to happen. This article will explore that reason in detail.

A few nights ago, my wife and I were driving along one of the lesser traveled highways. We came upon a person with a broken down vehicle in obvious distress. My wife said, "Maybe we should help". But I said, "I think not - it is not worth the risk". She responded, "But what if someday you were stranded and needed some help. Wouldn't you want someone to stop?"

Her reasoning is noble and her attitude is just exactly what our society needs. But her logic is faulty.

It is faulty on at least two counts. First off, my wife and I personally had much to lose and little to gain by helping this person. There would likely be time and expense involved to us in getting the stranger's car going again. There was some risk in that we could have been harmed by the person. The practical reward for all this was a possible future gain of being helped in a similar situation.

Secondly, how is the recipient of our compassion going to spread the word to the population that the two of us are compassionate people (so that we might be helped someday)? Of course, it would not happen. Helping this person would have no effect on our chances of ever receiving similar help in this large anonymous society we now live in.

That example illustrates a phenomenon that is ubiquitous to our society.

When an individual has reason to contribute to what is basically a group activity in which the benefits of the group activity are shared by the group, certain puzzling phenomena are evident that can only be described as "diabolical". While there is no generally accepted terminology for these phenomena, various manifestations are often referred to as the "Voter's Paradox", the "Volunteer's Paradox", the "Tragedy of the Commons", and similar terms. In this essay, these phenomena, which Hardin [1] described as "problems that have no technical solution" and others have termed as "social dilemmas" (abbreviated SD), will be lumped under one term -- "The Voter's Paradox" and abbreviated as VP. The "Voting Paradox", described herein, is an excellent representation of this class of phenomena.

The definition for "paradox" used in this essay is "a person, situation, act, etc. that seems to have contradictory or inconsistent qualities" from Webster's dictionary. Basically, what we have are two apparently contradictory truths in the same phenomenon.

Strangely, the "Voter's Paradox" manifestation seems to be a double paradox. The first can be expressed as, "while it is true that a particular endeavor would return a benefit to all members of the group where each individual would receive rewards that more than compensate for each individual's contribution, it is also true that any particular individual would receive an even greater net return by not contributing anything". I will call this the "freerider" aspect. This aspect of the phenomena is consistent with a related dilemma, the "Prisoner's Dilemma" which has received much study and is well reported in the scientific press.

The second paradox is that, "while it is true that the outcome of a group effort is made up of the sum of the individual efforts, in many cases a particular individual's contribution makes no significant and/or measurable impact on the outcome". I will call this the "my vote doesn't count" aspect.

Specifically, the claim here is that a situation can exist such that: (1); while everyone would be better off if everyone contributes (cooperating), a particular individual is always better off not contributing (defecting) and (2); the individual's contribution will not affect the outcome anyway. That both of these conditions are satisfied for a voter in a national election is obvious on reflection. We are all better off if most people vote, but my vote will make no impact and it does cost me to vote. Hence the term, "Voter's Paradox".

The reader should not be too quick to cynically regard this assertion as some academic pathological construct. On the contrary, the situation described is extremely common -- as I will attempt to show in this essay by providing examples occurring in all walks of life.

Related Philosophical Dilemmas

Some logical philosophers claim that the Voter's Paradox is a special case of another well known SD called the "Prisoner's Dilemma". In the Prisoner's Dilemma, a situation is described in which rewards are in amounts such that it would be in the mutual best interests of the participants for both to cooperate but the best interests of an individual is to defect. In particular, if you played the game over and over and you added up everyone's score, the total would be a maximum if everyone cooperated all the time. Yet a rational player is presented a payoff matrix that pays most for defection in every single play. The situation we want to discuss here, "The Voter's Paradox", is similar in the conflict in payoffs but otherwise is much different from "The Prisoner's Dilemma" -- and is much more common in the real world.

The VP phenomenon is generalized to include both contributions by an individual to a group shared benefit as well as the withdrawal of some portion of a group shared asset. The "contribution" example is best illustrated by the voting process itself, from which we get the name for this class of phenomenon. The "withdrawal" example is well illustrated by the so-call "Tragedy of the Commons" in which excessive withdrawals of a shared asset are done by certain individuals. This aspect is often called "freeloading" or "freeriding".

"Social Dilemmas"

Garret Hardin, in his essay, "The Tragedy of the Commons", -- discussed in the next section -- states that there are social problems that have "no technical solution", commonly referred to as "Social Dilemmas". In this essay, while concentrating primarily on the "Voter's Paradox", I will also examine this more general class. In particular, efforts will be made to identify characteristics common to all the known problems that fit the label "Social Dilemmas".

The General Component vs. Composite Problem

The SD seem to belong to a general class of problem that arises whenever an object is actually a composite of sub-objects which are essentially alike but very small compared to the composite. Consider the beach and the sand it is made of. Does removing one grain of sand make any difference to any practical description of the beach. Considering the fluctuations of the wind and water and other random phenomena, it is impossible to detect the removal or addition of one grain. The dilemma is that the event of one grain removed is not detectable but the accumulation of millions of grains removed is detectable. For further emphasis, consider the possibility that you owned the beach. Would you object if one grain were removed? Assume N grains have been removed. Would you object to the Nth +1 grain being removed?

Small increments of time added or subtracted are insignificant in a long term project. There is no way at the end of the project to determine if any particular person just stared at the wall one complete day, for example. But what if this were repeated thousands of times? You see the problem.

Setting arbitrary levels in a continuum creates the same dilemma. In our society, certain benefits accrue to a person if they have earned income less than some precise but arbitrary level. Let us say you are the administrator and you have a case where the potential recipient makes one cent more than that cutoff point. How can you justify not increasing the level by one more cent? It was arbitrary, right? Here is a person in need that would receive help if you raised it one cent. Why not?

The Classic "Social Dilemmas"

"The Tragedy of the Commons"

In 1968, Garret Hardin published his essay called "The Tragedy of the Commons" in which the conflict between group interest and self interest was clearly described. This classic essay shows the hopelessness of population control by using the example of a common pasture being shared by the local community in which access was free and without restrictions.

Each individual realizes that his best interests are served by putting as many of his cattle as possible on the pasture, even though the pasture has reached its carrying capacity and even though it is obvious that if everyone does this, the Commons will totally collapse. This, of course, is a classic description of the Voter's Paradox phenomenon.

Hardin's insight into this phenomenon has not been surpassed to this date. Some of his more interesting observations are:

He states that the problem is a member of a "class of human problems which can be classified as having 'no technical solution'".

"Freedom in a commons brings ruin to us all".

"Conscience is self eliminating."

The Prisoner's Dilemma

Melvin Dresher and Merrill Flood are credited with the first formulation of the "Prisoner's Dilemma" problem. This social model or game, as it is generally referred to in the literature, has a peculiar payoff matrix. In particular, the payoff is structured such that individuals "playing" the game would fare best, in total, if both cooperate, but the individual's best reward is always to defect.

A typical payoff structure might go like this:

If both parties cooperate, the reward is 3 units each.

If one party cooperates and the other defects, the reward is 0 and 5 respectively.

If both parties defect, the reward is 1 unit each.

An individual playing the game is faced with the realization that his or her best strategy is to defect regardless of the assumed decision of the other person! Put yourself in one prisoner's shoes: What should you do if you assume that the person is going to defect? If I defect I will get a reward of one unit but if I cooperated I would get only zero units. But what if he cooperates? In that case I should defect since that pays 5 units versus 3 if I cooperated too. I'm better to off to defect whatever the other guy does -- which makes for an easy decision.

An excellent description of this phenomenon is in the book, The Evolution of Cooperation, written by Robert Axelrod. [2]

Definition of the Paradox

Exploring all sides of the issue

It is the rule rather than the exception that the contribution a person would make to some group activity will exceed the benefit that individual might receive in return from being a member of the group. The voting example is a particularly good example of this phenomena in that it can easily be shown that one vote is highly unlikely to do any good whatsoever while there is cost to the person making the vote (admittedly small, usually).

The good news is that people do not always act "rationally" - in the sense just described. In fact, most of the time, enough people cooperate in these situations of public good such that the collective effort does not fail. [3]

In this essay I will try to comprehensively explore these conflicts between the interests of the individual and the group. I will examine the question of why, in situations in which collective action is involved, people do cooperate when it is often not it their best interests to do so. Actually it is more difficult to explain why people cooperate rather than not.

My attempt in this essay is to define the phenomena of the so-called "Voter's Paradox" (which I will abbreviate to "VP" for convenience) and related phenomena as clearly as possible. While it is recognized that the impact of the VP on our daily lives is enormous, [4] the primary purpose of this essay is to present the paradox itself in enough detail such that the phenomena can be clearly understood and evaluated.

When the VP is presented to most people, the typical response is "But what if everyone did that"? Upon the most casual examination, the question turns out to be quite ridiculous. If everyone chose not to vote then the election would fail. That's the answer, but it has nothing to do with the VP.

But let us examine the two possibilities:

1. Everyone behaves as usual. Result: my choice to not vote has no impact.

2. Everyone chooses not to vote. Result: my choice to not vote still doesn't do anything (Strangely, if I chose to vote, my vote might now be significant!)

The fact is, the only time my vote would have any impact on the election is when there is a tie -- a highly unlikely event.

Is there a problem of my action of not voting influencing others to do the same? Not very likely. It is very difficult for the private citizen to influence others even if he or she tried. Practically speaking, my actions in any group large enough for anonymity of the individuals, are not likely to have any impact on what others do.

The Classic Definition

Consider a group with two or more members and a situation in which the group as a whole would benefit from certain actions of the individuals in the group. While it is not necessary that the benefits be shared equally, we will assume that all members get some portion of the benefits and that the portion received by a member is not dependent on his/her contribution. The contribution of the individual is voluntary.

Under these conditions, so common to modern society, the payoff to the individual (share of group benefit minus his/her cost) is usually maximum when the individual does nothing at all!

Further, we can assume that if all or most of the members of the group contribute, all members of the group would benefit more than they would if there was no cooperation. That is, if most or all would contribute, the return for each individual is greater than it would be if each kept his or her contribution and proceeded alone. This is a valid assumption since otherwise there would be little reason to cooperate in the first place.

In summary, in this classic "individuals may volunteer but everyone shares the benefits" scenario, it is evident that the decision to do nothing is always the best strategy regardless of what the rest of the group does since the individual partakes of the benefits whether he or she contributes or not.

The Extensions to the Classic Definition

The classic definition, as described above, suffers from the criticisms that it is too general, leaves out some additional complicating details, and does not include real world secondary reactions that would impact a "rational" person's reasoning. An example of "complicating details" is the binary nature of elections. And many will suggest that secondary effects such as a person's reputation may completely override such "rational" decisions to be uncooperative.

I will try to examine these additional details by extending the definition in several ways.

Aspects to be considered
The Cost/Return equation

First, I will discuss the cost and return that a person receives in a cooperative investment. An equation will be presented that will attempt to quantify the cost/return relationship in a group effort. Of course, it is assumed that there will be some return, i.e., the effort will not be a total failure. If there is a chance of total failure, the equation would have to me modified by the addition of a multiplicative probability of success term.

Non-linear Payoffs

Second, various types of non-linear situations will be examined. For example, elections in which the outcome is binary. That is, the payoff is discreet and not proportional to the contribution. For example, we do not elect a president that is 40% Clinton, 35% Bush and 15% Perot. "Clinton only" is the payoff regardless of the percentages once his percentage of the vote is greater than any of the others.

Insignificance of Contributions

Thirdly, practicality will be considered. It is reasonable to accept that some returns can be so small as to be insignificant. When the water in Los Angeles is rationed and I violate the order to not take showers, the result to others will not be measurable. And if I feel real patriotic and decide to send Clinton a $1000 to help pay off the national debt - as one student did - the effect on the national debt is not measurable (a monitor on the national debt would not be able to detect that such a small contribution had been made). [5]

Fortunately, it does not require 100 percent cooperation for most group efforts to succeed. Many public projects function with only a small percentage contributing. Voting is a good example.

The Impact of Success or Failure of the effort

When a person contributes to a voluntary group effort, whether the effort will fail or succeed should be the first concern. Let us look at the two situations:

Suppose that enough members of the group make a contribution such that the effort succeeds. Then the defecting member will obviously receive maximum return by making no contribution at all.

Alternatively, suppose that essentially all defect. Then the particular contributing individual would lose even more since the return from his/her investment would be zero or worse (if the investment is not returned).

Extended definition of Cost/Return

Finally, the definition of cost and the return to the individual for a given action is extended to include any and all internal psychological feelings from the action. The good feeling coming from helping a person in distress or the bad feeling of running away, is part of the cost or payoff of whatever action the person takes and can be substantial.

Public Vs Private Solutions [6]

Many people that have the means to do so, accepting that an individual investment into the solution to a public problem nets a very minuscule return, take the matter in their own hands and sponsor a private solution. For example, if the community's public water supply is running low, rather than contributing to the public fund, a person may elect to put in his own pump.

Unfortunately, this is not a practical solution to the VP in the general case. It is easily shown that in many - if not most - real world situations, a cooperative effort is the most efficient. It is not practical for everyone to build their own roads and phone system. As we discussed earlier, investments often produce greater return when the input from many individuals are combined.

Even with a heavy load of freeloaders, group effort is often more productive than individual effort. Public television is probably a good example.

Manipulation of perceived values

In an effort to overcome the limitations imposed by the VP, leaders will often attempt to alter the perception of the values to be received. For example, we are constantly told that our vote will make a difference when in fact, a single vote makes no significant impact on any election.

Rational Behavior

The Rationale for being Rational

The theme of this essay is based on the concept that a person's best interests are served by acting rational. Rather complex philosophical arguments can be made that this may not always be the case. Some would argue that ignorance is best for most of humanity and evidence from recent history would seem to support this in that it appears that for much of the world, the loss of innocence seems to be closely correlated with diminished happiness.

These arguments lead in to a philosophical morass any study of which would greatly exceed the scope of this article. Therefore, in this essay, we will assume that it is in the best interests of an individual to be rational.

"Rational Behavior" defined

To make any progress in the study of this apparent dilemma, the concept of "rational behavior" has to be carefully defined. "Rational behavior" means that behavior that would actually provide a good return for the person's contribution - based on the currently available information (an action can be rational even if the information available is faulty or erroneous). This does not require optimality but does require that the return to the individual be at least equal to the cost to the individual. When there are alternate paths to take and a choice must be made, a rational choice would be the one that provides the best actual return to the individual making the choice.

On the basis of this definition, many actions would be classified as irrational even though the person taking the action was rewarded if the person's actions were based on faulty reasoning.

It comes as no surprise that a person's perceptions and/or a person's internal programming can cause irrational behavior - based on the above definition.

Limited Resources and Trade-offs

The person having unlimited resources is a rarity. By far, most of us are burdened by the fact that every contribution of time and/or resource to any particular action is at the cost to all other actions we might take with that time and/or resource. That is, when we ponder whether we can contribute $10 to some particular activity that would result in some reward, a rational person must consider the impact of the loss of that ten bucks to all other potentially rewarding activities.

Internal Programming

How a person reacts to the environment is determined by that person's internal programming. For the purpose of this analysis, that programming is considered to consist of two categories: genes and memes. An excellent discussion on both of these forces is contained in Dr. Dawkin's book, The Selfish Gene and other sources on the Internet. [7] For our purposes here it should be sufficient to say that "memes" are those psychological forces that become instilled in a person through learning and societal influences.

The Perceived Environment

The individual must act in any situation on his or her perception of the environment and the expected results of whatever action might be taken. That these perceptions are likely to be in serious error in many situations, is no surprise to anyone. The available data is almost always incomplete and often contaminated by others who wish to control the individual's action. Further, the analysis of this data by the individual is usually flawed due to the confused and improper internal programming of the individual making the analysis.

Of course, people don't act on just material rewards alone. The benefits that a person receives come in many forms, but the most common non-material benefit is likely to be "good feelings".

Good feelings

The good feelings that many get from making a contribution to the public welfare may be substantial and may exceed the cost considerably.

Is it a good thing?

Many people are motivated to contribute to a group activity if they believe that the activity is honest and useful.

My Reputation

"How will I be regarded by the rest of the community for the action I am about to take?" is a very powerful consideration for most people. Note, however, this powerful influence fades away when the community is large and the individual's actions are unknown.

The Motivating Forces behind Good Feelings
The Programming - Genes and Memes

The good feeling we get from doing any particular thing comes from our programming by our genes and memes.

The Current Environment

The psychological environment that a person is subject to has a great impact on the feelings that a person has about doing or not doing a specific act. For example, in World War II, a group of soldiers boarding a landing boat in preparation to attack an enemy occupied beach, knowing that there is little chance of survival, still do it. That is because that action is the only acceptable action in that current environment. But times change; in more recent wars, soldiers have refused to fight because the pressure to do so was not so great. Apparently the meme that says you should willingly give your life for your country has diminished in force over the years.

Our Perceptions

Whether we take a particular action or not is determined by what we believe the values of the variables in the cost-return equation to be - not what they might actually turn out to be. Our beliefs can change the perceived values of these factors enormously.

Judgments based on the imprecise knowledge of the future

Much cooperative activity that would be deemed as irrational if all facts were known may be still carried out if the future result is not known for certain but only as a probability. While a person would most likely not bother to vote if he or she knew that the potential winner was thousands of votes ahead and he/she was the only one left to vote, that person would still vote if the election details were still unknown or still to be determined even though there was reliable information that one of the candidates is expected to win by thousands of votes. For much of the population, "as long as there is some chance" that their vote will "count", they vote without regard for the incredibly small probabilities involved.

How we expect others to behave as a result of this action

Some people apparently believe that their actions will encourage others to do the same. This belief greatly impacts the perceived value of the group benefit.

The story of the motorist in distress given in the introduction to this essay is a good example. My wife wanted to help because we might need help in a similar situation in the future.

This implies that the person receiving the help will tell others of our act of compassion. They might, but will the word spread? Well, it doesn't seem to. Such acts happen all the time but they get little publicity. On the other hand, we constantly hear of robberies and mayhem.

We have to conclude that an individual act of compassion is not likely to have much impact on the mores of society in general.

When and if my car breaks down, there will be no noticeable result of my assistance given to a stranded motorist years ago in a strange city.

Ignorance ("extra-rational")

If cooperating is more beneficial to the group and its members, but cooperating is irrational for the individual, then ignorance (called "extra-rational" by R. Hardin) can actually be best for the group - a concept well known by governments and religions.

Detailed Analysis

If we hope to understand this apparent paradox, we must examine each of its components very carefully. While the end result appears to be paradoxical, each component, under careful consideration, is quite straightforward.

It helps a great deal to understand that the components of the cost-benefit equation are usually independent. In fact, the VP situation that is discussed here is principally due to this independence. On the other hand, if benefits are dependent on the individual's costs, then the situation is not likely to be a VP. Since this essay is about the VP, near independence will be assumed.

The Net Return

Let us define a few symbols to make the reasoning more concise and precise.


C = The direct personal cost of contribution

BG = Benefit to the individual derived from being a member of the group

BI = Benefit to the individual derived directly to the individual

R = Net return to the individual

Then for any action taken,

R = BG + BI - C

Again, I must emphasize that the most important fact to recognize in understanding the VP is that the components of R can be, and usually are, quite independent. I believe that a misunderstanding of this fact is the reason that many people have a hard time accepting and understanding the VP.

Further, since a person must act now on the basis of a future return, these variables represent perceived, not actual values. Obviously, the individual acts on what he or she perceives the costs and benefits to be, not what they actually are. This is very significant and will be discussed further in the following pages.


BG is the marginal benefit to the individual derived from being a member of the group and the result of this particular action. Specifically, BG is the individual's portion of the reward received by the group as a result of this particular contribution. BG could be a function of C but this article's purpose is to examine the case in which it is independent or nearly so. Societal benefits generally accrue to the individual whether the individual makes a contribution or not (unless no one or an insufficient number contributes).

If the group reward is finite or limited, BG is determined by taking the marginal reward to the group, as a result of the individuals particular action, and dividing it by the number of members of the group. Of course, this assumes that everyone shares equally -- which is often not the case but is an adequate assumption for this analysis. It should be noted that some group rewards are unlimited and BG would not be a function of the number of members. For example, let us assume that a reward for voting is freedom of the individual. The fact that others may enjoy that freedom does not subtract in anyway from my enjoyment.

More examples will be presented in detail later but for now a couple will be provided to illustrate the independence.

Community Center built from Volunteer Contributions

Our community wants to build a Community Center and to do it from contributions. I can contribute or not but in either case I still get to use the Center. Unless, of course, no one contributes (more precisely, the contributions are below some minimum value), in which case the community center will not be built. [8]

Volunteers save the Town by Sandbagging the Levee

I may volunteer or not but in either case, if the levee holds, my home will be saved just like everyone else's.


BI is the marginal benefit that the individual receives directly from her action without regard to the group benefit. An example follows.

Contribution to Public Television

A public spirited individual contributes $25 to Public Television and receives a Viewer's Guide. The guide is an immediate and significant benefit above and independent of the group benefits received from being able to watch the station.

Intangible Rewards

BI can be very complex to evaluate since it includes intangible "feel good" rewards. BI can vary enormously between individuals all doing the same thing. One person may receive great personal satisfaction for making a community contribution while another may not.

As will be discussed further in this essay, BI is greatly impacted by anonymity. In fact, anonymity appears to be at the very heart of the VP. If you make a public contribution and your effort is completely anonymous, many individuals would receive or feel very little reward. But if everyone knows about your contribution, BI in the form of personal notice and satisfaction can be substantial. In fact, the personal reward resulting from contributions to a small group in which each individual is known by the others can be of such value as to completely eliminate the paradox!


C is the cost to the individual for performing a particular action. For example, C would include the cost of driving to the polling booth for the voter. C can be quite small or even zero. Again, I must emphasize that BG usually has little or no dependence on C.

Like BG and BI, C should always be evaluated in a marginal sense. That is, what additional return will I get for this additional contribution? For example, a minimum contribution of $25 may get me coverage from the local volunteer fire department - an excellent investment. An additional $25 contribution may provide for a very slight improvement to service (actually, the same as the first $25) but the return on this marginal investment to the contributor is very poor.

Like BI, C is also greatly dependent on anonymity. If you live in a small community and you are observed chunking your trash out on the public highways, your personal cost can be considerable whereas in a large anonymous community, for many, the cost would be zilch.

The "Holistic" effects

An aspect of the extended VP, more common than not, is the situation in which the return to the group exceeds the contribution of the sum of the individuals. Of course, this is the basis for the overwhelming desire of most responsible citizens to have individuals contribute to the common good. The return we get from everyone or nearly everyone voting far exceeds the cost of the sum of the individual efforts. [9]

So, while group efforts can and often do result in a return less than the investment, most reasonable group efforts are characterized by the holistic effect, creating the diabolical condition of the VP.

Impact of Infinite Vs Finite payoff

Cooperative efforts can be classified into two distinct types: those that have finite return and therefore the return to an individual is diminished by the return given to other individuals and those in which the return to the individual is the same regardless of the benefits it provides to other individuals. And example of the second type of reward would be the repair of the levee that saves the town. That my neighbor's house is saved does not impact my benefit of having my house saved. In this case, the BG is not divided by the number of members.

The Impact of Non-linear Results

When individuals contribute to a group effort, the result is often non-linear (i.e., not proportional) with respect to the input. An example of linear results would be something like an investment group where the return will be proportionately better for every unit of input. An example of non-linearity would be the case of a petition effort to get a bill passed in Congress. In this case the result is binary, all or nothing, with no direct relation to an incremental input.

Many phenomena such as elections have a result that is binary in nature. The result is either true or false depending on the input reaching a minimum value. A politician is elected only if he receives a majority of the votes. This has particular impact on the phenomena of the VP in that it is highly unlikely that one vote will have any effect on the outcome. In fact, the number of votes can vary over a wide range without changing the outcome.

This means, for example, if you live in California and the votes collected back East already exceed what is needed to win the election, your efforts in voting have no impact on the result.

This situation is best illustrated by a simple experiment. Suppose that you had a balance scale with the balance pans filled with marbles with a sensitivity such that a one marble difference caused the scale indicator to go against one of its stops. If an equal number of marbles is in each pan, then the scale indicator is at center. Otherwise, the pointer is either at the left or right stop.

Suppose there are a few more marbles in one pan than the other (few being more than 2). I can remove a marble from either pan and nothing happens. Or I can transfer a marble from one pan to the other and still nothing happens. This example perfectly illustrates the VP for the situation where the results are binary.

"But my vote might break the tie"

It is difficult for people to understand what an incredibly small chance there is of a major election ending in a tie.

When there are probabilities involved, we must modify the cost/benefit equation to represent the expected value. This is done by multiplying the expected return by the probability of that return. [10]

The probability of a tie in a state election is infinitesimally small. And, if the election ends in a near tie, a recount will be called for anyway! National elections just do not end in ties!

How much would you pay for another vote?

One way to better understand the insignificance of one vote is to imagine that you are an active supporter of a certain candidate and you are out on the trail soliciting votes. How much would you pay for just one additional vote?

The Wasted Vote Myth

A better understanding of the VP might put to bed the specious argument heard so often in the last election that goes something like this, "I really would like to vote for Perot, but I realize that my vote would be wasted (since he is not likely to get enough votes to win) so I will vote for Clinton". This bit of choice reasoning, apparently used by millions of voters, supposedly made a major impact on the vote count in the last election. Note the fallacies: (1) Since no particular individual's vote will impact the election results, that individual would receive greater satisfaction by voting their "conscience". (2) The fact that many people considered a vote for Perot as being wasted and therefore switched their vote to another candidate significantly impacted the vote count for Perot and conceivably caused him to lose. We will never know.

The Impact of Large size with some randomness

In the real world, randomness is the rule rather than the exception. When the number of things in a collection is very large, the addition or removal of one of these things may be less than the normal random variation of the total quantity. This would make the addition or removal of one or two objects undetectable.

There are situations in which the impact of one event is just insignificant compared to the normal random variations. The amount of water I use to take a shower is less than the normal variations of the volume of water in the reservoir. Therefore, my taking of a shower has no measurable impact on the water situation.

A change so small it cannot be detected

While random variations can make detection impossible for one event, another factor is involved in the detection: the sensitivity of the detector. Even if there was no random variation of the water volume in the reservoir, no means of measuring the volume is sensitive enough to detect the usage of one shower by one individual.

But we are not in general talking about some device that does detection, but we are talking about human beings. If the event is not detectable by humans, then it is likely of no practical significance. The rock star on the stage cannot detect whether I clap or not. Most humans cannot detect if I say "aye" or not in a voice vote of 50 or so people.

Impact of group size

The VP seems to occur mostly where there are large numbers of anonymous members in a group. Those two factors -group size and anonymity - need to be examined more carefully.

The Size of the Group

A thoughtful person upon first examining the VP might speculate that the paradox results from the sheer size of the group. "My vote doesn't count because there are so many voters, the situation makes my vote insignificant".

So, how many votes does it take to make your vote insignificant. The answer is simple: your vote only counts when there is a tie.

Regardless of how small the number, your vote only counts when there is a tie, plus or minus one vote. Consider that there are 4 voters and you are one of them. If you did not vote and A got 2 votes and B got 1 then your vote could have caused a tie if you voted for B or done no good if you voted for A. If you didn't vote at all, then A wins. Regardless of the number of votes, this situation obviously prevails.

However, the benefit terms of the cost/benefit equations include such things as "good feelings", as discussed above which is a function of group size. That is, if I live in a small community, the "good feelings" rewards I receive are much more significant than when I am part of a large anonymous group. This negative impact on cooperation by anonymity has been discussed extensively in the literature. [12]

The Psychological Cost/Benefits

BI, the direct benefit to the individual and C, the cost to the individual, contain a component that we will call psychological rewards or punishment. For most individuals, psychological rewards and/or punishment are very powerful components in the cost/benefit equation. In fact, the factors account for most of the "irrational" but good behavior that civilization depends upon to exist!

Let's look at an example. Suppose your church wants to add a new audio/video room that will provide free access to educational materials. They wish to do this by means of contributions. How do you think the results would compare between allowing the members to contribute anonymously or to contribute to a basket being passed while all are sitting in their pews? I'm afraid anonymous contributions would not do very well at all.

Given that there are enormous social pressures to "do the right thing", what is the effect of anonymity in the group? It practically nullifies it. If I contribute to a cause and the contribution is anonymous, then these psychological factors are not at play. Other factors, particularly guilt, must account for this behavior.

In fact, this is why governments find it necessary to tax rather than rely on contributions for all causes, regardless of how worthy they may be. Once there is real anonymity, most people do not cooperate.

Behavior and the size of the group

The understanding that anonymity nullifies the psychological pressures to "do the right thing", then explains why people in small towns act in socially desirable ways and people in big cities typically do not. As long as most people in your group are fully aware of your actions, you will most likely act responsibly with regard to both personal and group activities.


If the logic presented so far in this essay is sound - especially the fact that a single individual's actions are of no consequence to the outcome and there is anonymity - then we must conclude that society will have a problem with "freeriders". And of course it does, with enormous costs in money, time and security.

While some actions are more sinister than others, we all freeload to some extent. Some of us might cheat Sears by taking back a product for exchange or refund when we actually did the damage. Why not? Sears is a big corporation and one returned item will not make any difference. Besides, they don't know me from Adam. Of course, I wouldn't even think of doing this to someone that knows me personally.

We cheat the insurance companies and the health plans that our dollars collectively support.

We take advantage of every benefit from the government we can whether we are justified or not.

In the view of some, more sinister examples are the cheating on welfare and the wasting of public funds and the goofing off by government employees.

Freeloading is a rational action when the "benefit-cost" value is positive. Public programs provided by the government, insurance companies and health plans provide great benefits compared to the cost to the freeloader. Society can increase the cost to the potential freeloader by changing the mental make-up of the individuals or by increased controls and punishments. It is most important to realize that these increased costs to the freeloader usually also greatly increase the cost of the benefits to everyone else.

An interesting aspect of the freeloader phenomena is that the freeloader can not exist without the contributions of those who do not freeload. The hippie living on welfare and using the public medical facilities depends on the existence of the straight people that they hold in contempt. That is, without the host, the parasite dies.


There are many asymmetries between the individuals of a group or between the group itself and the individual. For example, let us say that I can barely make ends meet and I contribute $100 to Public Television. My $100 is a great personal loss but an insignificant gain to the Public Television organization. Or, forcing Exxon to pay billions for the Alaskan oil spill benefits the local communities greatly while being fairly insignificant to Exxon.

How individuals value a cost or reward often varies greatly. Laws passed that makes some presently legal activity illegal, to help fight crime, often do more harm to the general population than to the criminal, for the criminal was already in violation of existing laws while the lawful citizen now has to restrict certain activities. Further the criminals are in relatively small numbers compared to the rest of society. The total group loss, therefore, is often much greater than the reward.

The Paradox in other Dimensions

The VP can raise its ugly head in time as well as space. For example, in a long project in which the end date is subject to significant variability, what difference would taking a day off make? That is, could the fact that an individual took a day off be detected at the end of the project? Not likely. (But what about "n + 1" days, and so on?).

Looking out for Future Generations

Why should I make significant sacrifices for the benefit of those yet to come? Even if I consume a great part of the Earth's resources and just leave garbage and contamination, I will likely not live to see the consequences. It is difficult for a rational person to give up very much for the generations that come after his or her death.

There is the possibility that our actions today may spell the end of humanity. What if our selfish actions today results in the destruction of the survival resources of the earth? What if the war machines we build create a very high probability that the Earth will be destroyed? Should I sacrifice my safety and immediate financial rewards?

Here we have a double whammy of the VP! First, will anything I do as an individual affect what the mass of humanity receives in rewards? No. Second, will anything I do affect future generations to come? Possibly, but I will not be here.

But what if everyone did that?

When most people hear the argument for the VP the first time, the most common reaction is, "But what if everyone did that?". Obviously, if everyone declined to vote, democracy would fail. Still the argument is specious. The impact of "everyone doing it" would radically change the analysis of any logical discussion. What if everyone decided to withdraw their money from the bank? What if everyone decided to quit buying new cars? What if everyone decided to not go to work tomorrow? What if everyone decided to read this article?

Thousands of examples can be given in which a certain action is harmless when committed by you and me but becomes a disaster if "everyone does it". Like I said, a specious argument.

If you owned millions of shares of IBM stock and you decided to put them up for sale, you would surely realize that your action is likely to result in lowering of the value of that stock. Many owners of IBM stock, including aging widows barely getting by, would suffer as the result of your sale offer. By the way, you would also feel the negative impact of this large sale if you retained some of the stock.

But what if you only sold a couple of shares? Most of us would agree, that offering of a couple of shares to the market is not likely to impact the value of the stock. But what if thousands of others followed your lead and did the same thing? If that happened, as with your large sale, the price is likely to fall.

Consider another case: let us say the Red Cross broadcasts a mass appeal for more blood as a result of needs coming from some disaster. What if you didn't feel quite up to giving blood at this time? Would their appeal fail? Of course not. But what if everyone followed your example?

While most people clearly understand the above arguments for the cases presented, they seem to have difficulty understanding the ramifications of other problems that are characterized by the same phenomena - the classic example being voting in a national election. Your vote in a national election has even less impact on the results of that election than the sale of one share of IBM stock would have on the price of IBM stock! And far less impact than your withholding of a pint of blood from the Red Cross.

Contributions via the "Pool" vs. Direct

Suppose that there are a thousand needy orphan children and a thousand contributors willing to give $100 each. Would it make a difference if this money were first pooled and then divided evenly among the orphans vs. the direct contribution of one contributor to an orphan? Yes, for with the "pool" method, it appears that my $100 will make little difference to any orphan and I might not contribute, whereas, I can see the great value coming from a direct contribution. [13]

Generalization of the Paradox

[Note: this section is far from complete!]

In the introduction, it was stated that this essay would attempt to examine the general case of problems that have the "no technical solution" (NTS) characteristic defined by Garrett Hardin. This section will examine the general case.

Minimal Requirements.

For the most general definition of the NTS problems, the only common characteristic seems to be the non-zero-sum of the payoff matrix.

Summary of known problems of the NTS type
Voter's Paradox

Non-zero-sum payoff

Insignificance of contribution (common, but not necessary)

Anonymity (usual, but not necessary)

Nonlinear (Binary) Payoff

Jointness of supply

Tragedy of the Commons

Non-zero-sum payoff

Non-jointness of supply

Volunteer's Dilemma

Non-zero-sum payoff

Very nonlinear

Jointness of supply (usually)

Arbitrary Cut-offs

Paradox of the infinitesimal change


Paradox of the infinitesimal change in time

Problems that are only partially NTS

When a thug steals from a bank, the theft obviously impacts all of the community that uses the bank. But does the thug belong to that community? Possibly not. In many cases like this, the perpetrator does not believe that he/she is taking from his own group but only taking from another group (possibly an enemy). In this case, the NTS phenomena does not apply.

However, there are problems in which there is some component of NTS involved.

Some non-voluntary problems are really voluntary -- at least, partially

Many would argue that much of the actions open to individuals of today's society are not really voluntary. For example, do we really have a choice in contributing to the poor when our contribution is actually obtained by taxation?

Closer examination of many "non-voluntary" contributions reveal that there is some, if not a lot, of voluntary aspects involved.

Requirements dictated by law can be avoided, for example. Many aspects of environmental protection are often avoided simply because the police cannot watch everyone at all times.

Laws can be changed.

Lifestyle choices can be made.

More Examples

[Note: This section incomplete]

Water Supply in Los Angeles

Public Housing Deterioration

Local Problems shared Nationally

If the problems of a local government (state, city, etc.) become the responsibility of the country in total, then we have the VP problem again.

The Littering Problem

What does one more piece of litter do to an already huge pile?

I'll pick up my litter but not the other guy's! How is this better?

Cutting off my nose to spite my face

Should I refuse to buy shoes made in China that I can get much cheaper than USA manufactured shoes even though I dislike China's human rights policy? Should I avoid buying Willie Nelson's albums because he is an alleged tax cheat even though I really like his music? Should I avoid buying products at Walmart's, which would save me a lot of money, just because some clerk got nasty with me once? Will Walmart ever notice my absence?

To take any of these actions causes me to lose direct and substantial benefits while having no significant impact on correcting the problems I dislike. I will keep buying Willie's albums.

Arbitrary Break Points

Break points are another baffling example of the conflict between the general and the specific, the whole and the atom. In rules, in government, in games, and in our personal budget, often levels have to be set that are arbitrary. How much can I allow myself to spend on entertainment each month? $200? How about $201? Why $200?

The so-called "poverty level", blindly followed and reported by the media (as if it were as absolute as the value of the gravitational constant!), is an arbitrary level. Yet it impacts thousands of lives. Let us say the government determines that the "poverty level" is $10,000 and you just happen to have an income of $10,001. What does the social worker do if you still ask for the "below the poverty level" benefits? She has to reject you! Buy why can't she bend the rules a little and allow you the benefits anyway? Well if she did, then she would have to consider the next person at $10,002 -- and so on.

Hand Clapping at a Concert

Hand clapping at a rally or concert provides a simple (if possibly silly) example that clearly illustrates the VP. The question to be answered is whether the person on the stage can tell whether one individual claps or not. It seems apparent that they could not but this could be easily confirmed by experiment for those who doubt. If I conclude that my clapping cannot be heard, then why do I clap? Direct pressure from those around me? Feels good inside?

Actually, while this example illustrates the insignificance of one "vote", it may not be a paradox if the person is directly rewarded by the good feelings from clapping.


[Note: This section far from complete!]

Hofstadter's Games


Bidder Game

Who ever bids highest wins unless a tie. Second highest pays amount bid. If tie, then go to next highest bidder. If all tie, replay the game.

Other Games



What are the consequences of the VP? How does it impact our daily lives? From the many examples given in this essay, the reader must surely agree that the impact is serious and universal. The choice between the individual's best interest and the group's best interest is a choice we all must make constantly. Apparently, we don't always chose what is best for society and ourselves even though we make rational choices!


If you have followed the above arguments and accept the logic, you should have no problem accepting the conclusion that most crime is a direct result of the "individual over individual's group" choice, as defined in this essay. That is, crime is usually committed based on the individual's assessment that the his/her benefit will exceed the personal cost. And that cost includes the damage done to society by this crime -- a society that the perpetrator must suffer with also. It would seem reasonable that crime will increase if either the benefit is increased and/or the cost is decreased. Most likely, the large increase in crime our society is now experiencing is a result of the decrease in cost to the criminal.

Can we blame the decrease in cost on the VP phenomenon? Unfortunately the answer is "Yes, very much so". The system imposes the cost and the system is composed of individuals that must weigh their cost/return ratio in every action they take. From the congressman to the cop on the beat, each individual involved in crime control knows that an action that would be good for society in general might be expensive to them personally. They defect. And when they do, the cost to the criminal just dropped another notch.

What about the crime itself? Do people ever weigh the cost of the crime to society (that they belong to) vs. their own gain? Surely they must. Surely, the person selling weapons or secrets to our enemies must evaluate their personal gain against the damage such a sale may do to our society.

Some examples of the cost to the criminal and potential criminal have decreased in modern times:

Social acceptability of criminal activity

In the last few decades, in many communities, crime has become more socially acceptable - even "cool". As we have discussed earlier, social psychological pressures are very powerful (enough to cause a person to sacrifice their life rather than be seen as a coward, for instance). This psychological good feeling of being admired by the individual's peers far outweighs the potential future destruction to the community in which all will suffer -- including the perpetrator.

Again, it should be emphasized that a person in the middle of looting and mayhem knows that their actions, one way or the other, will have no effect on the others committing these violent acts. Each person knows that if they abandon the looting, the looting will continue.

So why not join in? It would be nice to have a new TV!

Decrease in expected punishment


Reduced expectation of actually being punished



Socially unacceptable sexual activity is on the increase in spite of the widening of the definition of what is acceptable. In particular, sexual activity by the young and others in which the results present a burden to society are on the increase. Much of this is a result of the SD phenomena.

The increase is the result of both an increase in the benefit and a decrease in the cost. Some of the most obvious factors are:

Increased sexual pleasure

It is now socially acceptable for sex to be fully enjoyed - particularly by the female. Sexual activity is heightened by constant exposure to sexually stimulating media and dress.

Decreased Social Disapproval
Decreased amount of punishment
Decreased probability of punishment


[Note: This section is incomplete]

Politicians generally do what is in their own best interests with often disastrous impact on society in general -- even though they are a member of that society.

A large country like the U.S.A., composed of many divisions -- states, cities, communities -- is itself beset with problems of the SD nature. For example, why should my community send off money to the Federal Government to be distributed over the entire country? On the other hand, why should my community not pursue the fat government contracts that is an expensive waste to the rest of you, but a nice bundle of cash for our local folks?

In fact, why should a congressman do what is best for the country when his/her bread is buttered by the community he/she represents? How is spending ever going to be curtailed with each congressperson knowing this?

Why should a politician do what is best for their community when much greater personal rewards can be achieved in other ways?

Why should politicians return control to the states or the individuals?




Government burden and suppression of individual rights continues to increase since it benefits a few. Yet, we all suffer from these infringements, including those that benefit from it. Unfortunately, their direct reward exceeds their losses from being a member of society.

The Health Care Problem

Let's face it: while you agree that unnecessary and expensive medical tests are causing our health care costs to skyrocket, when you go to the hospital with that disturbing pain in your chest, you want the best that your insurance will pay for!

As long as health care is handled as an expense of the insured group or the government sponsored group, the problem will continue to get worse. The only hope to cure this problem is to remove it from the SD class and make health care and individual responsibility. Unfortunately, this creates other problems that our society is not willing to accept.

The Legal Mess

The SD phenomenon is ubiquitous to all aspects of the legal profession. "While I know that society in general will suffer if I sue the doctor for every mistake, real or imagined, I am going to sue his ass off!", we seem to all be saying.

It is said that juries make these huge awards because they would like to treated the same way if they were in the same situation.

And do not lawyers realize that they are part of the society that they are destroying with their greed? Sure they do -- but their personal take far outweighs the cost they feel from being part of society.

Ways to Remove the Paradox

Privatizing to the extent possible


Directly tying the return to the cost

The paradox goes away when a person is directly rewarded or punished by their actions. The strategy would be to delete or minimize the "group" component in the cost/benefit equation. That this is not always possible is recognized.

Small Groups

As discussed above, we have few problems with the freerider aspect of the VP when everyone in the group are personally acquainted with each other.

Coercion and other outside inducements

Garrett Hardin stated in his 1968 paper that the solution to the class of problems discussed here -- those having "no technical solution" -- is "mutual coercion, mutually agreed upon". Practically, this means government, hopefully a democratic government. But there are a few problems!

Using the Government to do your dirty work

Most activist groups use the government to enforce cooperation when it is obvious that voluntary cooperation will not do the job. Activism is not democracy, unfortunately.

Environmental Groups

Environmental groups know that there is little chance of successful environmental voluntary action by the population due to the VP phenomenon. So they have the government enforce their beliefs.

Funding of the arts

Those that would provide culture to the masses know that the masses would not support this by any voluntary sacrifice. So they use the force of law to give the masses what they "need".

Using Religion to induce cooperation

Religions have been quite effective in inducing people into cooperating and acting in the group's best interests. However, religion's technique of increasing the reward and/or punishment by promising an afterlife is not easy for many to accept. The force of religion as a means of invoking cooperation seems to be declining as the population has become more educated and "world-wise".

Using propaganda to encourage cooperation

The news media and the educational establishment has been quite effective in seducing members of society into "doing the right thing". The enormous guilt that many people feel if they don't throw their aluminum can in the recyclable bin is a testimony of the power of propaganda.

The disadvantage is that propaganda can be misdirected. Examples are too numerous to mention in this limited space!

Using the power of moral structures

[Note: This section is incomplete]

According to some philosophers, a meme based moral structure can induce cooperation and overcome some of the SD problems.


In this article, the various phenomena of the so-called "Voter's Paradox", or "Social Dilemmas" have been examined in detail. There are two major aspects to this paradox, both of which present enormous difficulties for a society based on social interaction. First there is the problem that it seems to be quite evident that certain scenarios requiring the cooperation of all or most of the individuals in a group would provide benefits for everyone far in excess of what they would be able to do privately. Good examples are elections, roads, water supplies, river levees and other large investments. Yet, at the same time, it is obvious that for a particular individual, his or her maximum return is obtained by making no contribution - that is, freeriding. For example, if the levee could possibly break, the individual would be best served by not contributing to the sandbagging at the main levee but instead working on defenses around his own home.

The second major component of the "Voter's Paradox" is that the contribution of the individual in large groups may be absolutely or practically of no significance. On a national election, one vote cannot possibly determine the outcome of the election. If the levee broke because it was shy 100 sandbags and I could only do 50, then my effort was useless. Or if it didn't break because it had at least 50 more than it needed, my contribution would again be useless.

Societal Problems resulting from the VP

Most of the major problems facing large societies can be traced to the VP. Massive non-cooperation results in a breakdown of many group activities that would be useful. The massive growth of the welfare roles, crime, government spending, government waste, and etc. are examples of individuals maximizing their own return at the expense of the group. The paradox is that they are acting rationally!

Solutions to these problems are difficult but possible. However, the purpose of this essay is to examine and to expose the problem - not to provide solutions. Understanding what the real problems are should go along way in helping to come up with these solutions.

Many do cooperate and that is often enough for success

That society functions at all is a testimony to the fact that a large part of society does "cooperate". According to R. Hardin [14], some experimental data indicates that about one half of the participants cooperate. I suspect that more cooperated in the past and less will in the future.

Fortunately, it does not require 100 percent cooperation for most group efforts to succeed. Many public projects function with only a small percentage contributing. Voting is a good example.

Another dilemma for society is that people are more likely to cooperate and not do what is in their personal best interest if they are ignorant and/or living lives controlled by myths. An educated person is more likely to be cognizant of the tradeoffs between self interest and group interest.

A meme supported moral structure could solve the "defection" problem. How to establish this required moral structure in modern society is a baffling problem, however.

Success can also be achieved for group activities that would fail if based on voluntary cooperation by invoking the force of law. Environment groups have made much use of this approach.

Privatizing and "pay-as-you-go" would solve many of the SD problems -- not without societal costs that some do not want to pay, however.


  • [1] Hardin, Garrett; "The Tragedy of the Commons", Science, Vol. 162; 13 December, 1968
  • [2] Axelrod, Robert. The Evolution of Cooperation. New York: Basic Books, 1984
  • [3] One explanation as to why people "irrationally" cooperate is the force of "memes". See "Evolution, Selfishness and Cooperation" by Francis HEYLIGHEN at the Internet Web site, <>.
  • [4] A discussion on the impact of the VP on society will be contained in another paper by this author, now in preparation.
  • [5 ]That is, random fluctuations far exceed such a small amount and therefore make it undetectable. In communications this is called "signal to noise ratio", which if too small, the signal cannot be detected.
  • [6] Hardin, Russell;Collective Action, John Hopkins University Press, Baltimore, 1982, Page 75
  • [7] Dawkins, Richard;The Selfish Gene. New York: Oxford University Press, 1976.
  • [8] See the Web site, "Principia Cybernetica", <> and "Memetics" at <>
  • [9] Most people, when first presented this argument, make a fuss over the fact that "my contribution just might be the one that will decide that the Center is to be built". This is extremely improbable for most real world situations.
  • [10] Actually, the return from a group effort can be less than the contribution as well as greater. There is no guarantee that group cooperation provides returns greater than the contribution. It is easy to imagine a situation in which the individual's efforts were wasted such as investing in a worthless development project.
  • [11] Hardin, Page 60
  • [12] See Glance and Huberman, "Social Dilemmas," Scientific American, March 1994, pp. 58-63.
  • [13] For an interesting analysis of this and more complex situations, see Derek Parfit, Reasons and Persons, Clarendon Press, 1984.
  • [14] Hardin, Russell, Page 29