Electoral Arithmetic

 Why The Way We Count Votes Makes a Big Difference and Why Third Parties Won’t Go Anywhere in the USA


by Jay Verkuilen*


           “Those who cast the votes decide nothing. Those who count the votes decide everything.” —Josef Stalin


           Many people lament the lack of political choice in the USA. I do not think they are wrong in that assessment.  However, it is clear to me—from reading the press and teaching—that the whys are much less well known. Some people assert that a two party system is “mandated in the Constitution.” This is untrue. The Constitution says nothing whatsoever about parties and says very little about elections, largely leaving things up to the state. In fact the size of the House of Representatives is only fixed by legislation at 435 and there is no constitutional reason that it could not be increased. Much of what we take for granted about our electoral system is not in the Constitution at all. However, the electoral rules we use do pretty much guarantee a two party system with relatively unfocused parties. Some even go so far as to say that this is a good thing. (It may be.  There are downsides to having a highly fragmented party system, as Italians or Israelis could tell you and as I will discuss below.) 



A Brief History Lesson


           Let us consider briefly the party system of the USA. Despite the misgivings of people like George Washington, parties emerged relatively quickly in our history, growing out of the conflicts between the Federalists and Anti-Federalists. In a very real sense, the debates undertaken by the Federalists and Anti-Federalists are with us today, as these two factions were the ancestors of our current political parties, though the roles each play have changed. For instance, about one hundred years ago the Republican Party represented many (if not all) of the same interests that the Democratic Party does today. The Republicans are the descendents of the Federalists, who argued for a strong federal government, while the Democrats were the descendents of the Anti-Federalist states’ rights-ers. Sometime around the New Deal things flipped because groups within each party’s coalition shifted. Republicans began to endorse the states’ rights position and oppose large federal programs because of their opposition to socialism and Keynesianism. Now the Southerners who used to be staunch states’ rights Democrats are all Republicans while African-Americans who used to be Republicans are now Democrats. 


           The last time a third party eliminated an established party was in 1856, when the Whig party fractured into pro- and anti-slavery factions. The anti-slavery faction formed the nucleus of the Republican party, which was initially an abolitionist party. There have been attempts to form third parties since then, but none have ever been successful except regionally, e.g., the Farmer-Labor Party in Minnesota and Progressive Party in Wisconsin, both of which were active in the first half of the 20th Century. There are a few other anomalies as well still (New York, for instance, which allows multiple party endorsements for candidates, or New Hampshire where Libertarians score well), but by and large, the USA has a two party system.



Why a Two Party System?


           However you slice it, the two parties have been with us for a very long time and it is unlikely they will ever go away or will fail to dominate the system. This isn’t just because they maintain a stranglehold on the electoral laws regarding voter registration, candidacies, etc., though those surely don’t help. The finger should, instead, be pointed at the seemingly trivial issue of how we count votes. Many reformers aren’t interested in such “process” issues, but they ignore process at their peril. One of the few iron laws of human nature is that humans will learn to exploit any incentive structure we find ourselves in eventually. Electoral rules, by providing structure, create incentives and people follow them and exploit them. 


           (I will gloss over details a fair bit here.) The French sociologist/political scientist Maurice Duverger first formulated what subsequently came to be known as Duverger's Law in the 1950’s, which summarizes the effects of different voting systems on parties.   Here’s a very simple example to illustrate Duverger’s Law in action.  Let’s say that we have to choose an electoral system. We will start with two logically distinct alternatives, winner-take-all, plurality rule, single member districts (WTA) and proportional representation (PR). In WTA, there is one district per representative (single member districts).  Whoever gets the highest vote total wins the seat from a district (plurality rule). In pure PR, there is one district for the entire country and seats are allocated in proportion to the votes cast. 





           Consider, for a moment, a distribution of opinion in a country.  Let’s say there are four blocs of voters, R, D, G, and B, and furthermore let’s say that roughly 35% favor R, 35% favor D, 15% favor G, and 15% favor B. (This is a very stylized version of my guess at the distribution of opinion in the USA today, with obvious labels for the parties.) In WTA, we end up with a toss-up between R and D candidates. G and B candidates never win.  This means that 30% of the population is consistently without representation in the legislature and within one given district, around 65% of the population wouldn’t have voted for their representative. 


           Let’s add a bit more complexity. Assume that these parties can be arrayed on a continuum of some sort such that G < D < R < B (again, directions have been chosen to be a stylized version of the USA). Thus, we have an ordering of preferences on a continuum. Being arrayed on a continuum is not an innocuous assumption to make. In fact it is frequently untrue, though the coalition-building arithmetic of politics tends to create them where they did not exist before. Someone who favors G would choose D as a second-best, R as a third-best, and B as a fourth-best. In short use GDRB to summarize their preference. B voters should go the other way around. It is a bit trickier in the middle and you could have a D voter with ordering DGRB, DRBG, or DRGB without the voter being said to be irrational in the sense that their preferences would be perverse from an ideological standpoint, e.g., DGBR. (Perversity here simply means “not responding to the assumed ideological gradient in a consistent fashion,” though it is hard to imagine how one might end up with a preference ordering DGBR.) There is lots of mathematics that occupy the time of people like me for many hours that one could do to analyze more complex situations. 


           If voters are sincere, they vote their genuine preference. Thus, even though G cannot win given the above distribution of opinion, a sincere voter would vote his or her conscience. Almost nobody does this, certainly in the event that it might matter. Voters are instead sophisticated and reason as follows: “Well I favor G, but G cannot win a WTA plurality election since it only has 15% of the vote. Therefore, I’ll vote for my second-best, D, and avert an outcome I want even less, namely an R victory.” This is basically “voting for the lesser evil” and is also known as tactical voting. B voters can be presumed to do the same thing as G voters. With the distribution of preferences listed above, we’re back to a coin toss between D and R. Of course when you have a coin toss, manipulation at the margins make a big difference, so that’s why you see various chicaneries of the 2000 election.  This is something that both major parties put a lot of effort into; currently the Republicans are better at it but we should not forget that Democratic stalwart the late Mayor Richard J. Daley, who turned the 1960 election for John F. Kennedy (possibly inadvertently, depending on who you ask). Things get even more complex when you factor in differential turnout at election day. 


           Of course, opinions are not simply fixed and given (exogenous in social science lingo), but adapt themselves to the given situation. You often come to like the choices that are presented to you over and over again, or simply forget about the existence of other choices. WTA, thus, has a natural moderating effect because it tends to pull the extremes into the middle. Lower percentage parties tend to cease to exist as they have strong incentive to merge with their ideologically adjacent party. The extremes attempt to discipline the moderates by saying “If you don’t represent the interests of G (B) we won’t vote for you anymore and then you’ll lose office.” Thus, the string of disgruntled third party presidential candidates over our country’s history. I highly suggest taking a look at the list of candidates historically sometime.  About every twenty years there are important third party candidates. In this system, coalition building takes place mostly before the election. 


           While no third party has actually eliminated a major party since the fracturing of the Whigs, it is a mistake to think they are not influential. The boundaries between the main parties and third parties are relatively porous. Ross Perot, for instance, was a disgruntled Republican, as was his less colorful predecessor John Anderson. Strom Thurmond when he ran for president and George Wallace a bit later were disgruntled Democrats. Pat Buchanan, representing similar interests to Thurmond and Wallace, is a disgruntled Republican. Ralph Nader is basically a disgruntled Democrat. With few exceptions, most people work within the established political system—why wouldn’t they?—until they become disgruntled and decided to protest in some way. One of the best protests is, of course, to ensure that your former coalition partners lose on election day. Splitting off from an established party is a way to punish one’s own implicit coalition partners. But these protests never seem amount to much because in the American system people want to run for President and don’t do the local party building efforts. 


           In addition to limiting the diversity of parties, WTA leads to extensive gerrymandering, that is, manipulation of the electoral districts in ways that advantage or disadvantage certain groups. See, for instance this map of the current Illinois electoral districts for an example of blatant gerrymandering, particularly the 4th, 15th and 17th districts. (One of the funny things is that this sort of gerrymandering is not allowed for state legislative districts.) Gerrymandering generally has the effect of disenfranchising certain groups. Again this is an issue on which all ends of the ideological spectrum play and indeed sometimes we end up with strange bedfellows of two ideologically disparate groups supporting the same redistricting proposals. 



Proportional Representation


           PR in its pure form, by contrast, has one electoral district for the entire country. Seats are assigned in proportion to the vote for a party.  If the population voted with the above split, roughly 15% of the seats would be held by G and B legislators, and roughly 40% of the seats would be held by D and R legislators. Since nobody has an outright majority, it would be time to build a coalition government, piecing together a majority out of various parties. Note that one big difference is that this coalition is explicitly constructed in the context of a given election. PR also tends to induce people to vote sincerely because their preferred party has a substantial chance of actually being represented in parliament and thus a possibility of being a coalition member. 


           Before singing the song of PR as a way to get “fair” representation, let’s think a bit. PR tends to emphasize parties, which in turn tend to represent issues as opposed to regions. One effect is that an individual legislator has little incentive to respond to local concerns, which is, of course, both good and bad. It’s good because many requests are from “special interests” who are looking for pork and handouts. It’s bad because citizens have no one to hold accountable for actions besides “the party.” Finally, legislators are often important interlocutors between citizens and government bureaucracies. When there are no districts, legislators have little incentive to do anything about citizen concerns. 


           Furthermore, pure PR often leads to fragmentation on single issues. The incentives of pure PR pulls the other way than WTA. If I’m disgruntled about the fact that some people can’t afford orange juice for breakfast, I can form the Orange Juice Is For All (OJIFA) party and run. If I get some votes, I’m in the legislature. If the small parties become an important part of the calculus of coalition building because there are many of them, as they are in Israel, for instance, they become unduly powerful in comparison to their size because they can bring the business of government to a screeching halt by threatening the coalition’s majority. This gives them incentive to play the hold-up game. It also means that many coalitions are highly unusual, to say the least, made up of fairly bizarre groups that would not be ideologically allied normally.  In other words, sophisticated voting gets pushed up another level.  


           Recognizing the potential for the hold-up problem and the desirability of regional representation as well as ideological representation, many countries actually have a mixed PR system of some sort, with some PR seats and districted seats, a minimum threshold (say minimum of 5% of the votes to get a seat), etc. This provides representation to broad national interests (parties) and local interests (districts) and has a useful moderating effect. In short, there are many complexities in real voting systems as the system designers try to balance various tradeoffs. My walk-away points, then:




What If the USA Had PR?


           The USA is one of the few countries in the world with a pure WTA system, which we inherited from the (at the time thoroughly corrupt) British electoral system.  Even the British are moving in the direction of PR. I consider PR to be highly unlikely in the foreseeable future, for both cultural reasons (we Americans are amazingly narcissistic and provincial about politics, far too often thinking that the rest of the world has nothing to teach us) and because the entrenched power brokers have no incentive to move the system. It might happen on a state level, however. How this kind of government would work with our powerful chief executives is another matter, though the French 5th Republic constitution is a good initial guess, I suppose. Even PR of some sort in the House of Representatives could make a big difference in terms of providing representation to groups in the population. 


           That aside, let us run a simple thought experiment. Assume that the USA were to switch to a PR system. What would happen? Would the religious conservatives and business interests that currently make up the cores of the Republican party stick together? Would the coalitions of labor, ethnic minorities, and upper middle class professionals that make up the Democratic party stick together? I think it is highly unlikely. My guess—and it is only a guess—is that the USA would end up with four large parties, much like modern Germany, which is also a regionally and ideologically heterogeneous society. Germany has two large parties:  The moderate right Christian Democratic Union (CDU), which is a fusion of Lutheran and Catholic parties, and the Social Democratic Party (SPD), a socialist/labor party. It also has two relatively significant, the Free Democratic Party (FDP), which is a classical liberal party, and the Green Party, which is a New Left party built out of the environmental movement. Post-war Germany had coalition governments of CDU and FDP, SPD and FDP, and currently SPD and Green. 


           Four parties: Christian, Business, Labor, and Green. The names themselves don’t really matter. What would be the benefits of this? Well for one thing more people would be willing to vote their conscience since their views would have a reasonable chance of being represented in Congress. In the 2000 election, for instance, I wrote in John McCain because I was disgusted with both major party alternatives and feel that the Green Party is too left (I’m basically a conservative Democrat, if you care). This was a total throw-away vote, of course. I do not think that in a close election for a local office I cared about I would ever do this but would instead vote in a sophisticated fashion.  Furthermore, with actual institutional membership in legislative bodies, the different interests would have explicit representation. When someone from the Business party said something, it would be a lot clearer exactly who paid for the statement, for instance. What about presidential elections or senate elections? If multi-party endorsements were more broadly allowed, e.g., like in New York, it would be possible to have, say, a Christian/Labor candidate for president. Alternately—much harder to manage of course given how difficult —would be a runoff electoral system for president, again like most of the rest of the world.  This is not without its pitfalls, as we saw with the French election last year when sincere voting on the Left got out of hand, leaving Jean Marie le Pen in the runoff. No electoral system is perfect. But the American one could be a lot better than it is. 



For Further Reading


http://www.wikipedia.org has several informative articles on the topic, some of which I cited above. 


Robert Dahl (2002). How Democratic Is the American Constitution? New Haven: Yale University Press. Nearly anything by Robert Dahl is worth reading. 




*  Jay Verkuilen holds far too many degrees for his own good, including a PhD in political science. He is currently obtaining another in quantitative psychology. Like ninjas, he mostly spend his time at airports getting sucked into jet engines, but hopes one day to make a lot of money teaching MBA students how to do statistics.