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The Perfect Voting System

By       (Page 1 of 1 pages)   2 comments, In Series: Balanced Voting
Follow Me on Twitter     Message Paul Cohen

It is no surprise that the perfect voting system, one that will solve all problems, is a pipe dream. Clearly no voting system will turn lead to gold or square the circle, and it turns out that among all the other things we cannot expect from a voting system is that it will prevent strategic voting. For all practical purposes, that is the conclusion of Gibbard's theorem so we can rest assured that it would be a waste of time and energy to search for such a system.

But more than saving us time and mental energy, the theorem stimulates thinking about what form strategic thinking might take in an election using, for example, Balanced-Approval voting (BAV). Recall that with this voting system, a voter may mark any number of candidates either as support or oppose. The winner is chosen according to which candidate has the largest net support, net support being defined as the number of opposition votes subtracted from the number of support votes. In reality, voters have a third option as well. With respect to each candidate, the BAV voter can also abstain.

An important virtue of BAV is that it avoids coercing voters into inventing some rational (such as electability) for evaluating candidates. Voters are encouraged to vote based only how they feel about each individual candidate. Still, some people just cannot keep themselves from looking for an edge, some way to gain an advantage over others through some clever strategy. They may just feel blessed by great luck and cannot imagine being a loser or perhaps they just enjoy the game and feel that playing and losing is the next best thing to playing and winning. It seems safe to say that even with BAV there will likely be efforts to game the system.

Electability Raises its Ugly Head
Electability Raises its Ugly Head
(Image by Paul Cohen)
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BAV voters can be expected to show support on their ballot for each candidate that they hope will win election and they will mark oppose for all of the candidates they hope will lose. It is hard to imagine that a voter could find a good reason to scheme by moving a candidate from support to oppose or conversely from oppose to support, but it is not so hard to imagine a voter revising an abstain to something else. For example, a voter might decide to mark a candidate as oppose instead of abstain not because the voter actually opposes the candidate based on merit, but instead out of concern that the candidate in question might win election instead of a candidate the voter does honestly prefer. So electability can raise its ugly head even in BAV elections.

It is doubtful this would be the only way of voting strategically in a BAV election, but it seems likely to be the most common situation. The effect will be to disadvantage candidates who are projected as likely winners; but maybe these prominent candidates deserve a handicap. In compensation though, there will likely be some people who will vote support for a predicted winner, only to satisfy some emotional need to stand with a winner rather than any consideration of merit. Although this motivation for a switch from abstain to support is not exactly what we might think of as strategic or tactical voting, it actually does meet the conditions of strategic voting in the context of Gibbord's theorem.

Whenever a voter chooses to abstain on a BAV ballot, that choice will rest on where the voter decides to draw a line. One voter might limit support votes only to candidates that voter sincerely wants to win and perhaps also limits oppose votes to only candidates that the voter sincerely wants to lose. But there will be other voters who feel very reluctant to exercising the abstain option. And there are many possibilities between these two extremes. In view of this, it is surely unreasonable to expect two voters who share exactly the same opinions about the candidates to necessarily vote exactly the same. And that is not really such a bad thing.

BAV allows a voter only to support, oppose or abstain with regard to each candidate and some voters are likely to feel that to properly report their thinking, they need more than those three choices. That thinking is no doubt what motivates the adoption of ranked voting or of score voting. But the proper objective for an election is to sample the opinions of all of the voters and fortunately that does not require a fine and detailed measure of each individual voter's opinions because statistics can come to the rescue. Those finer details of opinion will weave into election outcomes as many voters with like views will inevitably make different choices about where to draw lines on either side of the neutral middle position.

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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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