A hypothetical Indiana voting scenario comparing alternate voting methods

by Paul Hager

The best way to really understand how different voting methods can produce radically different results is to look at an example. Accordingly, I have put together the following scenario that represents a hypothetical race in 2004 for U.S. Representative in Indiana's 8th District. I chose the 8th District because I've run for office twice there and have a reasonable idea of what the voting patterns tend to be. I've made a number of simplifying assumptions so as to prevent the example from getting too complex.

For this scenario, I've posited the creation of a new political party, which I'll call the Libercrat Party. The Libercrat Party has managed to get a well known and popular Hoosier to run in 2004, which allows the Libercrat candidate to run a competitive race with the Republican and Democrat candidates.

For simplicity, we will assume that there is one major poll done a month before the election that is reported by the media throughout the district. That poll asks the following questions:

  1. If the election were held today, who would be your first choice for U.S. Representative?
  2. If you have a 2nd choice for U.S. Representative, who would that be?
  3. Are you Republican, Democrat, Libercrat, or Independent?

Based upon these questions, the newspapers report the following breakdown:

It's pretty clear from the news reports that, although the Libercrat is doing much better than typical third party candidates, there still isn't much chance for the Libercrat to win. The reason is that the optimal strategy for the Libercrat's supporters is to defect to the candidate closest to their position who has the best chance to win (see below for discussion). In the general election, the Libercrat's support bleeds away and the final vote is 47% for the Republican, 41% for the Democrat, and a dismal 12% for the Libercrat.

The newspapers only focused on the results of question 1, which makes sense because in the plurality voting method that is used in Indiana, the only preference voters can register is for their top candidate. But the 1st place information doesn't accurately reflect which candidate the voters really prefer, as we can see when we look at all of the data.

The actual voter preference found by the poll breaks down as follows:

With the more complete poll information, we now see that there are 10 categories of voters with varying candidate preference rankings. When we look at those preference rankings, we get a very different picture of which candidate was preferred by the voters than was indicated by the news media.

Let's start off by comparing the Republican with the Democrat using the following method: whichever of two candidates is ranked higher based upon the polling data will get that category's votes. The Democrat's support was 30% Democrats (26% yellow dogs and 4% dem-libs) + 4% Democrat-leaning Libercrats + 7% of the Democrat Independents or 41%. The Republican's support was 25% Republicans (21% hard right + 4% rep-libs) + 4% Republican-leaning Libercrats + 10% Republican Independents + 8% Libercrat Independents or 47%. So the Republican beats the Democrat head-to-head.

Now, let's compare the Libercrat with the Democrat. The Democrat again gets 30% Democrats, but now only gets in addition the 7% Democrat Independents or 37%. The Libercrat gets the 12% Libercrats + 8% Republican- and Democrat-leaning Libercrats + 4% rep-libs + 8% Libercrat Independents + 10% Republican Independents or 42%. The Libercrat beats the Democrat head-to-head.

Finally, let's compare the Libercrat with the Republican. The Republican gets the 25% Republicans + 10% Republican Independents or 35%. The Libercrat gets the 12% Libercrats + 8% Republican- and Democrat-leaning Libercrats + 4% dem-libs + 8% Libercrat Independents + 7% Democrat Independents or 39%. The Libercrat also beats the Republican head-to-head.

The above breakdown based upon the voting preference is called the Condorcet method, and is the consensus best system (according to voting science) for determining the true preference of the voters. The Libercrat in our hypothetical example is called the "Condorcet candidate" or "Condorcet winner" because the Libercrat beats all other candidates head-to-head. (Note that it is possible for there to be no candidate who defeats all others head to head. This occurs when there are intransitivities in voter preference or "cycles" - that is, A beats B, B beats C, and C beats A. Variants of the Condorcet method have different ways of resolving cycles to select a winner, which I won't get into here.)

We know that with plurality voting, the Libercrat loses. In fact, it has been demonstrated in voting science if the Cordorcet winner is not ranked in the top two in pre-election polling, the Cordorcet winner will probably lose the election. This is because in a non-cooperative "game" such as an electoral system, the optimal strategy with the plurality method is to defect to one of the top two candidates since they have the best chance of winning (i.e., voters choose the "lesser of two evils").

Suppose that some misguided reform lobbyists are able to get the Indiana General Assembly to adopt the Instant Runoff Voting (IRV) method in 2003. IRV is actually a method called the Single Transferable Vote, renamed. It is a ranked system in which the candidate who gets the majority of 1st place votes wins. If there is no majority, the lowest ranked candidate is eliminated and the votes are transferred to the remaining candidates. This continues until a candidate gets a majority. If we run the above scenario using IRV, the very first thing that happens is that the Libercrat, who is the lowest ranked of the three, is eliminated and those votes are apportioned between the Republican and Democrat. In life, as in our hypothetical, IRV will frequently fail to pick the Condorcet candidate. IRV also has a propensity for monotonicity paradoxes. This means that if voters switch the ranking of their preferred candidates, it can actually cause the candidate they don't like to win. Typically this will work to the disadvantage of third parties. Together, these problems make IRV a very bad voting method and one that should never be considered as an alternative to the plurality method.

Now let's assume that knowledgeable reformers are successful in getting Approval Voting (AV) adopted in 2003, and run our scenario again. We make the following assumptions: whenever a voter actually expresses a preference order (such as Republican and then Libercrat) that voter will utilize AV and vote for both candidates; if the voter expresses a preference for only one candidate, then the voter will "bullet vote" or cast only one vote for said candidate and no additional approval votes. Based upon these assumptions, we get the following vote totals:

The Libercrat wins the approval vote by 53% to 47% to 41%.

For completeness, I'll throw in one more voting method that no one is talking about for elections, although it is used rather extensively in college sports. It is called the Borda Count, and like Condorcet and IRV, it is a ranked voting method. With Borda, rankings are weighted such that for N candidates, the 1st place ranking is N-1, 2nd is N-2, and so on with the lowest being N-N or 0. The NCAA uses the Borda Count when sportswriters vote on team rankings.

Here's how things break down:

After all of the 1st and 2nd place votes are tallied, the Republican ends up with 82, the Libercrat 81, and the Democrat 78. In this instance, Borda doesn't select the Condorcet winner. In Condorcet's famous critique of Borda's method, he demonstrated that Borda will often fail to pick the candidate who can beat all others head-to-head. An important caveat is that AV will not always pick the Condorcet winner either, though it will do so most of the time. However, in its favor, AV is not subject to intransivities the way the Condorcet method is.

If Condorcet is really the best voting method, why am I not pushing for it to be adopted? It is a matter of simple pragmatics. Any ranked voting method will require a completely different ballot, a very different way of voting, and redesigned voting machines. Each one of these requirements is a major hurdle to acceptance by the electorate, and a weak point that opponents of reform can exploit to prevent adoption. AV doesn't involve a substantially different way of voting - people already vote for multiple at-large candidates. AV doesn't require a change in the ballot nor an expensive modification of voting machines. By pushing AV, serious reformers have a good chance of actually fixing the electoral system in a way that will benefit society.

Final note. In designing the above scenario, I attempted to come up with something that was realistic without being so detailed as to be incomprehensible. The strength of Democrats, Republicans, and Libercrats was based upon national polling data on the two parties and voters who have expressed a desire for a third party. How the people in the middle break down was based upon a competitive race in the 8th District in which the voters are primarily concerned with pocketbook issues like taxes, Social Security, and the economy. The erosion of support I use in this example is fairly typical. For example, in the 1968 Presidential race in which George Wallace made a strong showing, he lost around 50% of his support as measured by his high water mark poll numbers compared to his final election result. In 1980, as I indicated in Why I'm running for Secretary of State, John Anderson went from around 40% approval to 7%. Although neither Wallace nor Anderson were Condorcet candidates in their respective races, a 3rd place Condorcet candidate can expect to share their fate.