Stephen H. Unger

3/11/07

#### What is the Problem?

Let's start with a few examples suggesting that the most common voting system may not always yield the best results.

Example 1. A 2-candidate election in which 5 people favor A and 4 favor B (multiply the number of voters by whatever constant you like to make it more realistic). Clearly A should be chosen. Well, maybe not so clearly! Suppose the election is for a city council seat and that A is greatly disliked by the 4, perhaps because of one particular issue that the other 5 don't care much about. Assume that the 5 favor A over B by only a very small amount (they like B almost as much as A), and that the 4 B-supporters are very negative with respect to A. Then, if A is chosen, 5 people will be happy and 4 people will feel bad. If B were chosen, 4 people would be happy and the other 5 would feel pretty good. Wouldn't B be the better choice? Before considering an election method that would result in the second outcome, let's consider another case.

Example 2. An election with candidates X, Y, and Z, where polls indicate that most voters will vote for X or Y, with Y having a bit of an edge. A substantial minority (perhaps 20% of the electorate) believes strongly that Z is much better than X and Y. Further assume that this minority considers Y to be somewhat worse than X, altho they think X is also pretty bad. This group is truly between a rock and a hard place. If they vote for Z, the candidate they truly believe is the best one, then Y, the candidate that they think is the worst one, will probably win. If they vote for X, then X, only marginally more satisfactory to them than Y will win, and the chances of Z building up strength in the future will be diminished. This is generally referred to as the lesser evil dilemma. Sometimes, in an election with leading candidates X and Y, there are two minority candidates, W and Z, with very different views. W and Z supporters all feel pressure to vote for what they consider "lesser evil" candidates, one group considering this to be X and the other Y.

#### Saying More with a Vote

The common voting scheme illustrated above is called plurality voting (PV). Whoever gets the most votes wins. Where more than two candidates are likely to get substantial numbers of votes, the PV scheme may be modified to include a runoff feature that is activated if no candidate gets a majority of the votes. There would then be a runoff election between the top two vote getters. This is sometimes called delayed runoff.

The drawback of PV is the same as its main advantage, namely, simplicity. It allow voters to indicate which candidate they prefer, but not the strength of their preferences. A straightforward alternative to PV, that fills this gap is range voting (RV). In an RV election, voters can assign a number to each candidate that expresses how strongly they prefer that candidate. These numbers are usually integers in some limited range. For example an integer from 0 to 9. If there are 5 candidates, a particular voter might feel that A and B are both very good and not prefer one over the other, that C is not as good, but still quite acceptable, and that D and E are both terrible. So the voter might give to A, B, C, D, and E, respectively 9, 9, 7, 0, and 0 points. There is wealth of information about RV and related topics on the range-voting website initiated by Warren Smith.

If RV were used in the first example, one might imagine that 5 voters each give A 9 points and B 8 points, while the 4 voters give the two candidates 0 points and 9 points respectively. The score for A would then be 45, while B would get 40+36=76. So the winner would be B, reflecting what we might call an overall higher level of satisfaction with B. The disappointment, or regret, felt by the 5 supporters of A is smaller, even when aggregated over a larger number of voters, than the more intense regret that the B supporters would have felt if the election had gone the other way. The supporters of the losing candidate, rather than being annoyed with the use of the RV system, which deprived them of a small added pleasure, might more reasonably consider that in some future election, they will be the beneficiaries of this more sophisticated scoring system. Certainly, over a large number of elections, the average level of satisfaction will be substantially greater. There is an important problem with RV, but let's postpone discussing it until after we see how RV works with the second example--the lesser evil case.

Recall that the winner will almost certainly be X or Y, so that, in a PV election, those who much prefer Z feel constrained to vote, not for Z, but for X, who they dislike, but who they think is not quite as bad as Y. Range voting rescues them from this need to betray their favorite. Now they can give both X and Z 9 points and Y 0 points. The 9 points given to Z in no way improves the likelihood of the greater evil candidate Y winning, so they need not hesitate to give the maximum score to the candidate they like best. In an RV election, there is never a good reason not to give your most preferred candidate a maximum score.

A consequence of this feature is to increase substantially the votes cast for third parties. Candidates of such parties are still unlikely to win elections, but the fact they they receive significant numbers of votes is likely to get them more notice, and people are more likely to pay attention to their positions on issues. They can therefore exert more influence on public affairs, and may even have a chance to grow to the point of becoming serious contenders for office.

#### Problems with RV

One problem with RV is that it depends on voters voting according to their true feelings. If, in Example-1, the majority wanted to have their way even at the expense of the minority, they could maximize the chances of their slightly preferred candidate winning by simply giving A the top score and B a 0. The greater the number of people who behave this way, the more likely it is that others, with opposing views, will follow suit. Those who behave this way in one election may spoil the chances that they might be the beneficiaries of a genuine RV vote in the future. The effect of such tactics, called "strategic voting" by students of voting systems, is to cause RV to morph toward AV, or even further, toward PV. Perhaps the most likely outcome is that the ratio of strategic voters would range between one and two thirds. But this is just a guess, no hard data is available. It seems plausible that, as long as a substantial number of voters in an RV election assign weights reflecting their true feelings, that the results, while not as good as they would be if all votes were sincerely cast, would be noticeably better than what might have been expected for a PV election.

The situation resembles, to some extent, an iterative version of the prisoner's dilemma, where, if the prisoners cooperate, they both gain, otherwise, they both lose. An important difference is that in the RV case, there is generally no direct evidence indicating that some set of voters has acted strategically.

Another important, tho not as fundamental, drawback of RV, is that tallying the votes is more complicated. It would not be terribly difficult using machines, but it certainly would slow down manual counting. The actual voting process would also take longer, as the voters now have a more complex task.

#### Small Scale Voting

In the above discussion, it was tacitly assumed that we were talking about political elections, where the electorate is substantial. But there are many other situations in which people vote. Some examples are judges rating contestants in a diving event, faculty members voting on which of several applicants to invite to join them, faculty members voting on which of several students to honor with an award, and a board of directors voting to choose a new CEO for the company. In many of these situations, those voting know about different aspects of the candidates. They may have less rigid views about them, and be more willing to be influenced by the views of their colleagues. A caucus voting to choose candidates for a political party is another context in which range voting seems to be a good tool for choosing someone best representing the views of the party membership. In cases of these types, range voting would often be a very effective way of tapping the collective wisdom of a group, so as to make the best choice. Strategic voting should be less of a problem. Since the number of voters is small, tallying is much less of a problem.

In some situations, there may be a large number of candidates on the ballot, some of whom are not well known to many voters. A more sophisticated version of range voting allows voters to abstain on candidates they have no opinion about, rather than give them a low, perhaps 0 score. In such systems, candidate scores are computed as averages, rather than sums. An annoying problem with this is the unlikely, but possible, situation in which a "stealth" candidate is entered, who is unknown to all but a few voters (perhaps relatives!) all of whom give that candidate the top score. If everyone else abstains on that person, the winner would be a virtual unknown individual! This possibility can be ruled out by requiring that the winner must be rated by some minimum proportion of the voters. But what should that minimum be? How about 50%? Perhaps this feature might best be implemented only in elections with a small number of voters.

#### A Stripped Down Version of RV

While range voting seems like a very attractive idea, getting it adopted in real political elections would be very difficult. To my knowledge, no jurisdictions anywhere in the world use RV. Certainly the fact that it sounds complicated and would increase election costs is an important factor. So it might be useful to start with a simplified version.

The simplest possible case is RV with range 0, and 1. This has a name of its own: approval voting (AV). It is easily described by saying that voters simply indicate subsets of the candidates that they approve of, or consider acceptable. So, if there are seven candidates, a voter might check 3 of them (assign weights of 1), and reject the other 4 (assign 0 weights). An AV election might be thought of as an ordinary PV election in which over-voting is allowed. The winner is simply the candidate with the most 1's.

AV effectively solves the lesser evil problem, since, as in the case for a larger range, approving one's favorite candidate cannot help elect the candidate one dislikes the most. It also helps with cases such as Example 1, since if the majority favoring A also likes B, it is likely that many of them will vote for B as well as for A. Approval voting seems to be a clear improvement over PV, while being no more costly. Adopting it would therefore be a positive step in itself, and, if people like it, could also help get a more sophisticated version of RV adopted at a later time.