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Obstruction of Voter Expression


Paul Cohen
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The all too familiar plurality voting system gives voters a quite acceptable way to express themselves in elections;

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Warning - This passage must be kept free of obstruction at all times - sign
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sadly though, only when there are fewer than three candidates. When there are three or more candidates, the spoiler effect illustrates clearly how plurality voting becomes inadequate. The spoiler effect results from voters being so restricted in how they can express themselves that the data collected in election ballots is inadequate, allowing election outcomes fail to be what the majority of voters would have preferred.

The defining example of the spoiler effect involves three candidates, two of whom are regarded as equally satisfactory by a majority of voters. The voters are clear in their minds that they would prefer the election of either candidate A or candidate B over candidate C, but they do not care so much which of A or B turns out to be the winner. Perhaps 60% of the voters prefer A-or-B and 40% prefer candidate C. But in the plurality election these 60% of voters are forced to choose between A and B. The vote is likely to split mores or less evenly between A and B, and as a consequence, C is declared the winner. What the plurality election delivers is at odds with what the majority of voters want because the plurality election system provides no way to discover, much less act on the fact that a clear majority of voters actually prefer either of A and B to win rather than for C to win.

Instant Runoff Voting (IRV), has been quite successfully promoted, largely based on claims that it is the way to eliminate any danger of this "spoiler effect". Voters are asked to rank the candidates and in the example, it is reasonable to assume that the 60% of voters would rank A and B as their top two choices. The votes are tallied to simulate a series of two elections and if A loses in the first round then the A votes will shift to B in the second round so that B will win with 60% of the votes. Likewise if B loses the first round then A will win with that same 60%.

Does IRV eliminate any worry about the spoiler effect? Surely it does if the meaning of the "spoiler effect" is limited to elections with at most three candidates. But in an earlier article, we find an example that we might well call the "spoiler effect" if were it not an IRV election with five candidates. A recent article argues that such a defect actually occurred recently, distorting the outcome of an Alaskan primary election. These different examples of the spoiler effect occur when a voting system fails to allow voters to fully express how they feel about the candidates; with IRV, like with plurality voting, an election goes awry, seemingly because the voting system restricts voter expression in a way that can corrupt an election. That, rather than the example, should perhaps serve as our definition of the spoiler effect.

In the case of IRV (or any of the many other ranked voting systems) a difficulty is that voters often feel that two or more candidates are equally satisfactory but nonetheless they are obligated to rank them in some order of preference (or not rank them at all with possibly worse consequences). Unless a voter opposes such similar candidates more than any others, IRV voters must fabricate a (false) preference for one candidate over the other. A second deficiency of ranked voting systems is that sometimes a voter dislikes a candidate and ranked voting systems, like plurality voting systems and even approval voting, provide voters no way to express their opposition clearly.

In earlier article s I have claimed that evaluative voting systems (i.e., systems which ask voters to rate the candidates without in any way obligating them to compare candidates, one to another) avoid the spoiler problem; I seem to have been mistaken about this. AV does not force voters to choose between similar candidates, but still, AV does lack a proper way for voters to express opposition to particular candidates. Voter opposition does matter and a responsible voting system should take care to measure it effectively. AV fails to do this and that leads to another example of the spoiler effect.

AV simply asks voters to indicate which of the candidates they support. They can support one, two or even all of the candidates. To be clear, AV voters are asked to choose, for each candidate, whether to support the candidate or to withhold support for that candidate. Advocates of this system are quick to point out that in effect, this makes it possible with AV to vote against a candidate and that is by specifying support for every one of the other candidates. That claim does have merit because, in terms of the vote-count, decreasing the vote-count of a candidate has the same effect on the election outcome as increasing (by one) the vote-count of all of the other candidates. But what if a voter opposes two of the candidates? Though with AV, a voter can, in effect, cast a vote of opposition, that trick works for one candidate only; moreover exercising that option comes at the unacceptable price of, in effect, disallowing the voter to express anything whatever about the other candidates.

The earlier example of the spoiler effect can be turned on it on its head in an AV election. Suppose there are three candidate A, B and C and also suppose that while 40% of the voters actually oppose all of the candidates, they also find candidate C to be the least objectionable of the three choices. These 4000 (figuratively holding their noses) vote approval of C while abstaining with regard to A and B. In contrast, the remaining 6000 voters feel that C is the worst of the three candidates. Of those 6000 voters, 3100 vote approval of their favorite candidate, A , while the remaining 2900 voters vote approval of their favorite candidate, B. So candidate C (whom not even one voter actually supports) wins in this AV election. 4000 voters (who figuratively held their nose while voting) prevailed, even though 6000 other voters would have preferred either of the remaining two candidates. Sadly those 6000 votes were split nearly evenly between A and B. Once more, the problem is that Approval voting has no way of detecting, much less acting on, the fact that 6000 voters opposed candidate C.

Balanced Approval Voting (BAV) is similar to AV but it allows voters the alternative of declaring, for each candidate, either opposition or support; and as with AV, voters have the alternative of declaring, candidate by candidate, to specify neither alternative. How would the last example change if it had used BAV instead of AV? The 4000 voters who disapproved of all of the candidates would probably choose to vote in opposition to both A and B while abstaining with regard to C (this is consistent with how these voters feel so there would not need to hold their noses for this). The other 6000 voters who find little difference between A and B, will declare support for both (though, in no way affecting the outcome, some might instead vote opposition to C). Either way, the election would end as a tie between A and B. Election officials may have to flip a coin to decide between A and B, but perhaps that would be unnecessary because a handful of voters would vote differently than described above. Unlike with AV, in this election with BAV, election results will reflect the will of the majority of voters. In large part this is because voters can adequately express their preferences and the election outcome can reflect those preferences.

These examples show how important it is for a voting system to allow voters to fully express their opinions through their ballots. Might BAV lack some as yet unrecognized need for greater expression that somehow could corrupt elections? That cannot be ruled out, but if so then that would signal a need to seek out a yet more expressive approach to voting.

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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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