Selecting an Ambiguity Resolution Procedure

Even if it is granted that we should use CondorcetThe general term for any election method that uses ranked ballots and has, as it's first princple, the Condorcet Criterion: any candidate which beats every other candidate individually must win the election. Any Condorcet method must come along with an ambiguity resolution procedure for cases in which there is no winner by this first criterion. as the fundamental election procedure, there is substantial difficulty in deciding which resolution procedure should be used. To begin, we should certainly obey the following rule.

Any ambiguity resolution procedure must only be applied to candidates in the Smith SetThe Smith set is the set of candidates on which a Condorcet ambiguity resolution procedure acts. It is formed by finding the smallest group of candidates such that each candidate in the set defeats each candidate not in the set. This is the natural second step of the Condorcet process, since all ambiguity lies exclusively within this set. (mouse over for description).

This criterion should be trivially obvious, and it is essentially the furthest we can carry the spirit of the Condorcet CriterionAny candidate that would defeat every other candidate in a one-on-one runoff must win the election. This is simply a restatement of majority rule. in ambiguity resolution. This rule has not been applied in any of the examples considered, since all have had only three candidates. In essence, this rule simply stipulates that majority should rule as far as it’s decisions are consistent with each other.

Once the candidates have been reduced to the Smith set, which is a real election would most likely not be much larger than the minimum size of three, there is literally no fool-proof way to procede, simply because we are dealing with a incomplete information. As discussed under The Paradox, this incomplete information is necessary to avoid strategicA vote is called "strategic," "tactical," or "pragmatic" if it does not reflect the voter's true preference, but is rather an attempt by the voter to secure the best possible outcome, given the voter's prediction of how other voters will act. voting; there is no way to gain any more information from voters with their own best interest in mind. Therefore we have to do some guesswork. The following are the methods we have considered on this website. The latter three of these are methods that are cited as non-Condorcet methods, but they are certainly also valid as ambiguity resolution techniques.

• MinimaxThis is an ambiguity resolution system in which the winner is the candidate whose worst defeat is best. Intuitively, the idea is to pick the candidate who was most nearly a Condorcet winner in the sense that even their worst defeat was closest to being a victory.
• Ranked PairsIn this ambiguity resolution system, all pairwise defeats are ranked in terms of strength. The defeats are then examined from strongest to weakest. The strongest defeat is “locked in” but ranking the winner above the loser. Each defeat is then examined, and if it does not violate any previous decisions, it is also locked in. This is a bit subtle. The intuition is that we should regard each defeat as sufficient cause to rank the winner above the loser, but since this cannot be done for defeats, we at least ensure that it is done for the defeats of strongest margin.
• Approval VotingThis system is the most basic extension of traditional plurality. Rather than selecting a single candidate, voters simply select one or more candidates of which they “approve,” in effect voting as many times as they want, but only once for each candidate. The winner is the candidate who receives the most votes, pure and simple.
• Instant RunoffThis election method is based on the principle of being able to initially vote for your preferred choice, and then transfer your vote to more viable candidates if your first choice cannot win. Like Condorcet methods, IRV begins with a ranked ballot. Initially, all first choices are tallied, and if one candidate wins a majority, they win. If no candidate has the majority, then the candidate with the least votes is eliminated from all ballots (wherever that candidate was the first choice, the second choice becomes the new first choice) and the process begins again. It is called "instant" in comparison to other election systems where a series of "runoffs" are held, reducing the pool of candidates each time. In instant runoff, the voters need not return to the polls, since these runoffs can be performed instantly using ranked ballots.
• BordaThe Borda method is a means of giving different numbers of “points” to various candidates, so that one can choose one candidate as their distinct first choice but still lend support to others. Typically, a ranked ballot is used, with the voter’s first choice being given the greatest number of points, and each subsequent candidate receiving one fewer. The winner is the candidate with the most points.

Note that for the final three methods to be used, some modification of the vote-counting process would be necessary. For approval voting, voters would need to be able to indicate where their approval "ends" in their ranking. Also, for all of the last three, it would be necessary to look at ballot again in order to tabulate results, since the matrix of pairwise comparisons does not provide enough information by itself.

All of these methods have merit to themselves as resolution procedures. Since there is no way to analyze all the factors involved in an election, the most utilitarian result is not information that we can gain from ballots, and as a consequence there is nearly no way to judge which of these is most in keeping with Condorcet principles. There are three different ways to choose which procedure to use.

Decision Procedure: Elect a Method

This is perhaps the most obvious thing to do, and the latter two suggestions would not occur to most (and indeed do not seem to be advocated in any sources we have discovered). The most important thing is that the citizens feel confident in the election method being used, so that results will have legitimacy. Therefore, the various methods are put to a vote using whichever system is currently in use. Initially, then, it would be decided by PluralityThis is the voting system currently used for most American elections. Each voter chooses only one candidate, and the winner is the candidate with the most votes., but if we later wished to change methods, we would elect a new method using the method currently in place.

Decision Procedure: Vary Methods by Election

This is much more unorthodox, and much more unsavory at first. Essentially, a set of resolution procedures would be chosen, and a different procedure would be used for each subsequent election. This seems counterintuitive, but only because there is a tendency to believe one method is right, and should always be used. No method is right. Since there is the possibility that different methods might favor different types of candidates, such a rotation would achieve a sort of equal access. This leads into the third, most unsettling, but ultimately most sublime, idea that we propose.

A Revolutionary Decision Procedure: RANDOMNESS

In this procedure, which ambiguity resolution technique would not be decided until after votes are cast, but some random technique. Of course, fraud would be a serious concern, so great lengths would be necessary to ensure the citizens trust the random selection: a very public and carefully observed lottery device, for example. A better idea might be to use a pseudo-random process, based on an easily verifiable phenomenon. For example, the first decimal place of some publicly availible but chaotic number, such as the Dow Jones Industrial Average. This would be an easily verified phenomenon, and impossible to falsify (except by a rather immense conspiracy).

This idea seems abhorrent, but consider the implications for a moment. First, as discussed above, it does not compromise the result, since all methods are to be equally regarded. Second, this method would eliminate strategic voting, something that no “deterministic” procedure can accomplish. Any strategic vote necessarily depends on the particular resolution procedure, because it tries to “trick” the system into giving the desired result. If the voter does not know how the system will operate until after casting a vote, it would be complete guesswork, and certainly it would be impossible for enough voters to perform the exact same guesswork to change the result of the election.

This site does not exist to advocate attempting to implement this plan. The reason it is not brought to the fore, and indeed to the front page, of this website is simply because very few people would take the website seriously and read on. However, it is our hope that if you seriously consider these ideas, you will understand that this is the single most revolutionary idea proposed on this website. So long as the “candidate” resolution procedures are chosen so that the potential strategies conflict exactly with each other, this is a practical solution to a previously thought unsolvable problem: an election procedure with no strategic voting possible. It of course is not rigorously a solution (though with enough analysis, it might be made one), but for all practical purposes the problem is solved.

Through randomness we can unlock untold order: a unification of honest and pragmatic voting, bringing untold clarity and accuracy to electoral results. Now is not the time to advocate this idea. But should a citizenry ever be so enlightened as to accept it, a great obstacle in the history of Democracy will finally be met, and Condorcet's ParadoxThis paradox is that in some situations it is impossible to obey majority rule in an election. The situation in which paradox can arise is what is called a majority rule cycle. This is when, according to the result of the election, there is a cycle of candidates, each beating the next in a runoff. Imagine the simplest case: there are three candidates: A, B, and C. A majority rule cycle occurs when A defeats B, B defeats C, and C defeats A. This is a paradox because to install any one of these three candidates defies majority rule, since there exists another candidate which the majority prefers. burst open.