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How Biased is IRV?

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In principle, an election pretends to determine how citizens feel about some issue; usually it is to find out which of several candidates to choose one or another public office. Elections resemble what a polling company might want to do, usually taking a much larger sample but sampled a bit mindlessly, without due corrections or even recognition of the value of taking a random sample.

But surely, at a minimum, the raw data taken in an election should accurately reflect voters' actual opinions. However, in the previous article of this series, we showed how voting systems other than balanced voting systems, tend to fail in this respect. In essence this is a failure to consider a wide enough range of possibilities of how voters might feel about a candidate. Instant Runoff Voting (IRV) is not a balanced voting system so this criticism fits it, but there are additional anomalies that are peculiar to IRV which further contribute to miss-reading voter opinions.

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IRV is described in an earlier article, but in brief review, voters are asked to list candidates in order of preference, starting with the candidate the voter prefers most over all others. The problem is that voter opinions quite often cannot be accurately described by such a list. A given voter may not even have a clear preference for selecting the first entry of the list. Instead, the voter may find that two or even three candidates seem equally satisfactory; how can such a voter express his or her opinion about which one is first? And when the ballots are tallied, the ordering of the lists is a critically significant matter. Moreover this objection can apply not only to the first entry but just as well to every other position in the list.

So IRV voters cannot always avoid providing misleading information on their ballots. To make matters even worse these forced errors may not even be random. Rather than drawing straws or flipping coins to decide where to place a candidate, voters seem likely to do what is easiest and that is to rank the equivalent candidates in the order they appear on the ballot. This creates a bias in favor candidates who appear early on the ballot surely and that is an invitation for abuse. For convenience we will refer to this issue as the equal preference dilemma (EPD).

Generally, voters will be concerned only about the relatively few candidates that they particularly like or particularly dislike and many if not most voters will include them all on their list in an effort to best express their feelings. But particularly careful and informed voters will know this to be a mistake. These few voters will know to scrupulously avoid listing any of the candidates they oppose but instead to include at the end of their lists all of the candidates they don't know or don't care about (though again, probably ordered as they appear on the printed ballot). As noted in the earlier article, this potentially widespread voting error disadvantages lesser-known candidates such as those from small parties. This other problem we will refer to as the intuitive voter problem (IVP). One cause of IVP is the lack of any way for a voter to explicitly and effectively express opposition to specific candidates.

In the first of several rounds involved in tallying IRV ballots, only the first-listed candidate on each ballot is counted; the candidate who has the smallest tally (of these first-choice entries) is rejected and will not considered in the remaining rounds of the vote-tally (an example from an earlier article shows that, unfortunately, this very candidate could be a consensus candidate who deserves to win). Successive rounds of single-candidate elimination are held counting only the first candidate on each list who has not yet been eliminated.

One might consider a modification of this runoff system as a way, perhaps to speed up the counting while reducing the harm done by EPD. We could eliminate multiple (let's say three) candidates at a time by including in the tally not just a single candidate but the top three candidates who have not yet been eliminated. Of course the number would have to be adjusted downward from three for the last round of counting to make sure a winning candidate would remain.

This would only reduce, but in general not eliminate the damage from EPD though it will not help at all with IVP. EPD will be a problem for all ranked voting systems and that IVP occurs for any ranked voting system that permits voters to submit an incomplete ranking list (as is nearly always the case). So both of these defects are apply to Borda systems as well as IRV.

Of course, we could (by choosing a larger value, not arbitrarily three), reduce the tally iterations to a single count of the ballots, and this would completely eliminate the effects of EPD. The resulting vote-tally would seem to be the same as for approval voting (AV), but as noted above, IVP would remain a problem. The reason is that the voters, still being asked to construct an order of preference list, and representing preferences as an ordered list is what drives the IVP errors (while it also inflicts extra effort on voters).

Conceptually, AV seeks the same information from voters as the simplified one-step IRV system. AV simply does a better job of collecting that information accurately, thereby avoiding the conditions that cause IVP distortions. With AV, voters are not asked to construct an ordered list of voters, but rather just a list of which candidates the voter can support. With AV, neither IVP nor EPD is any concern. Even so, AV is not balanced, so it still suffers from a failure to allow voters to distinguish between the two very distinct forms of not-supporting a candidate. Avoiding that kind of bias requires a balanced voting system.

The reduction of IRV to AV by the simplification sketched above can easily be adapted to see how BAV could be interpreted as a similar, single-step simplification of IRBV, And these two systems are balanced. IRBV does still ask voters to prepare an ordered list of candidates, but the order is by importance to the voter rather than an order of preference. Because opposition to candidates is explicit with IRBV, preparing the list should be considerably easier for voters than in the case of ranked voting, though with many candidates it would still be a chore (that is avoided with BAV). Neither BAV nor IRBV suffer from EPD or IVP distortions. This illustrates why I have suggested that balanced voting might appropriately have been described as unbiased voting.

IRV has a particularly high potential for collecting and deciding elections based on erroneous information from voters; in many instances IRV makes that unavoidable, though well informed and particularly conscientious voters would be able to avoid contributing IVP errors. Balanced voting systems simply avoid such problems by providing voters a way to more fully express their opinions, including both support and opposition to candidates. Particularly important is that with balanced systems, voters who wish to remain neutral regarding individual candidates have an easy and natural way to exercise that option.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)

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