In this article we will consider, for several different voting systems, what about them might cause voter distress. In pursuit of brevity we limit the discussion to a single voter and only a very limited number of voting systems, but the examples might serve as some food for thought.
Elections aim to be accurate measures of voter's attitudes toward the candidates, so it seems reasonable that how the voters feel about elections should be a serious interest and consideration. This encroaches into the concerns of psychology and sociology, however, and that makes this a clear departure from the tradition of treating voting systems as mathematical objects.
We focus on elections with five candidates in which our voter, V, favors two of these five candidates, F1 and F2 but is strongly opposed to two other of the candidates, D1 and D2, both of whom she feels are not at all acceptable. There is a fifth candidate M and V feels ambivalent about M. For V, a win by M would be clearly preferable to a win by D1 or by D2, but she does not really feel M would be a good choice and she would much prefer a win by either F1 or F2.
Plurality voting is quite familiar to all of us so that we consider first. V approves of both F1 and F2, and with plurality voting V has to choose between them. Perhaps she prefers one of them slightly over the other and that could be the deciding factor. But she may have read the polls and knows that the one she does not prefer is the one that is more likely to win. Consequently, she may choose to vote instead for the candidate she prefers a bit less. But possibly the polls suggest that the contest will really sort out as a contest between M and D2 so she may be swayed to vote for a candidate, M, despite the fact that she does not really want M to win. Clearly V may find that deciding on one candidate to support quite stressful.
The next most widely familiar voting systems are the ranked systems like IRV where the voter is asked to rank the candidates in order of preference. V knows that, provided if votes according to the instructions then F1 and F2 should be the first two in line and that M should be third. With IRV she would be best advised not list D1 or D2 at all since her vote could, at the end of the counting process, be a vote in favor these candidates. But V may nevertheless list them at the bottom as a way of emphasizing that they are her least favorite candidates.
But notice that in choosing whether F1 or F2 is listed first, V is faced with much the same issues as with plurality voting; does she list them according to her very slight preference for one over the other? Or is there some way she might take into consideration the polling results she has read about? Quite possibly these considerations will cause at least some pondering about possible consequences if not some distress or a mental flip of the coin, but there will be considerable consolation that she can at least vote in a way that denies support to both of the candidates she strongly opposes.
Third in line among voting systems when listed by familiarity would be approval voting. In this instance, V is presented with a list of candidates and is asked to check off which of them she supports. Clearly she will check off her two favorites, F1 and F2, but what about M? She does not support M, but what if her reading of the polls suggests that the contest will boil down to whether M or D2 will win? V might decide to fib a bit and also check off approval of M. Contributing to the defeat of D2 may seem worth the price of committing that small fib, but what if the polls are wrong and her vote contributes to a win by M over A1? Considering that possibility, V could find that making the choice is an emotional challenge.
In my last comment to the preceding article I gave the name XMAV to a voting system that from one point of view is a trivial modification to Approval Voting. In this system, the voter is asked to vote either for or against each candidate but significantly, the voter is given no opportunity to remain neutral -- other than by staying away from the polls and just not voting at all. Wanting to participate in the election, V is forced to either vote for M or vote against M. She may mentally flip a coin, appeal to divine guidance or consider whether there is some strategic play in choosing to vote one way or another but whatever her approach, checking either box (support or oppose) seems to her to be a troubling lie.
In another minor modification, but this time to XMAV, the resulting system is Balanced Approval Voting. As with XMAV, the voter is asked to fill, for each candidate, either a "support" or an "oppose" box. But with BAV, voters have the option (not available with XMAV) to check neither box (or both boxes) as a way of remaining neutral with respect to a given candidate. With this system, the natural way for V to vote is to indicate support for both F1 and F2, opposition to both D1 and D2, and neither support nor opposition to M. This accurately expresses V's position with respect to all of the candidates. It is still possible that V may decide on some way to vote strategically, but this voting system does not force her to do so. To V at least, this minor change to SMAV makes a big difference.
These examples may seem interesting but it is an easy mistake to read too much into them. They are all based on just one particular voter and following different voters through the same voting systems it is inevitable that different issues will arise. For example, a voter who actually does have strong opinions that completely determine a ranking of the five candidates in strict order from first to fifth place might very well find it a challenge to compress those five ranks into just three.