Summary: Each voter casts a standard, preferential ranked ballot. It is not necessary for the voter to give a complete list of preferences, however like most ranked systems doing so increases the effect the voter has on the election results.
Insanity Voting is meant to capitalize on both strategic voting and strategic nomination. While other systems attempt to minimize the strategy considerations allowed to voters and potential candidates, Insanity Voting instead realizes that strategic elements are an advantage and instead attempts to maximize it. The method: Assign each candidate a number from 1 to n - do this in a way such that the voter knows the candidate's number before voting, perhaps by sorting them alphabetically. To determine the first winner, convert each voter's first preference into a number from 1 to n based on the candidate he chose. Sum them up, divide by n, and take the remainder - the winner is the candidate whose number matches (or the last candidate if remainder 0). To determine the next winner, examine each voter's second preference with respect to his first, and determine their difference. If a voter voted for candidate 5 first and candidate 8 second, the difference would be 3. Add n if the result is negative. This in turn generates a second number from that voter's ballot ranging from 1 to n - 1. Remove the previous winning candidate from the selection pool and assign each candidate a new number (original number - 1) if they had a higher number than the previous round's winner. Sum up the numbers from the ballots as we did before, divide by n - 1, and determine a new winner. This process is then repeated until you have as many winners as you want. In fact, you can even generate a complete ordering of all possible candidates this way, and you're guaranteed to never have a tie, something that isn't possible even in plurality methods. Strategic Voting: Insanity Voting, as stated before, is completely vulnerable to strategic voting, even when done by a single voter. This is by design, as it greatly increases the impact an individual voter will have on the election results, and therefore increases the incentive for turnout. Similar arguments have been used to support the electoral college, for instance, however insanity voting increases the odds an individual will have an effect on the election outcome to their absolute maximum possible. To vote strategically in Insanity Voting, you must dishonestly change your list of preferences until your preferred order of candidates wins. Note that it is possible to change your preferences such that _any_ selection of candidates wins, regardless of the other voters. Strategic nomination is similarly egalitarian - unlike most other methods, which tend to ignore the fringe candidates that don't receive any of the vote, in Insanity Voting every candidate matters equally. Insanity Voting allows for both teaming, spoiler candidates, and crowding. Criterion: Neutrality of Spoiled Ballots: Passed. Each unmarked ballot (or preference for an incomplete ballot) will have no effect on the vote. Arrow's unrestricted domain or universality Criterion: Passed with flying colors. The winners are all ranked, in order, and can be from any of the candidates listed. Moreover, the outcome is completely deterministic, not random. Arrow's non-dictatorship Criterion: Passed. Arrow defined dictatorship to be only counting one ballot and ignoring the others. In Insanity Voting, every ballot is counted, and every ballot determines the winner. One might call this dictatorship of the entire electorate, and that seems far more preferable than tyranny of a mere majority. Arrow's non-imposition or citizen sovereignty Criterion: Passed as well. Every candidate can win - in fact, it's quite likely they will. Summability: Passed. Insanity voting is first order summable, the best kind. We can cut it up into however many districts, counties, or polling places we want, and we'll be able to break each voter's ballot down into a series of n numbers on the first try. Plurality criterion: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of election must be no less than B's.": Passed. Since all candidates always have an equal chance of winning, this criterion holds. Favorite Betrayal Criterion: "For any voter who has a unique favorite, there should be no possible set of votes cast by the other voters such that the voter can optimize the outcome (from his own perspective) only by voting someone over his favorite.": Passed, for two reasons. If we assume the voter is voting strategically, then for any and all sets of votes by others, he can elect his favored candidate. If, on the other hand, the voter isn't voting strategically, it should be noted that he cannot alter the probability of his candidate winning anyway, and thus can't possibly betray him. Pareto criterion: "If every voter ranks candidate A above candidate B, then B must not be elected": Failed, except when there are two candidates and an even number of voters. And that's a pretty common exception, really - the best way of passing. Participation Criterion: Depending on the definition used, this one is either passed or failed. Mike Ossipoff's overly restrictive definition, "Adding one or more ballots that vote X over Y should never change the winner from X to Y" is not met. However, Douglas Woodall's definition, "The addition of a further ballot should not, for any positive whole number k, reduce the probability that at least one candidate is elected out of the first k candidates listed on that ballot" is met. It should also be noted that an inverse of the participation criterion, that choosing to vote and rank your candidate can cause him to win, is always true regardless of the makeup of the electorate - in other words, one always has a complete incentive to vote, no matter how unpopular his candidate is. Independence of Irrelevant Alternatives: Failed. However, many fairly good methods fail this criterion too. Later-no-harm Criterion: Passed. All candidates have the same probability of winning regardless of what you put on your ballot, so adding him later will do him no harm. Mutual Majority Criterion: Failed. However, any subset of a majority of voters can vote strategically and select their preferred candidate. In fact, it only takes a very small subset of just one person. Condorcet and Generalized Condorcet Criterion: Failed, however we could modify the method to select a Condorcet winner if one exists, then default to insanity voting. That seems to be all the rage these days. Consistency Criterion: Failed, unless the selected winners are the last candidates. But that only seems fair, since they had to be listed last on the ballot. Monotonicity Criterion: Failed, but that's not a problem since Instant Runoff and similar methods fail it too, and most insanity voters will probably want to vote strategically anyway. Strategy-Free Criterion: Failed, but that's ok because strategic voting is important to have in an election system. Additionally, another Criterion that I believe is important enough to be listed that I couldn't find anywhere: Impossibility of Ties Criterion: The voting system should never rank two candidates equally or resort to nondeterministic methods to resolve ambiguity. And, of course, the criterion specially made up for the Insanity Voting System: Insanity Criterion: Every voter must be capable of affecting the outcome regardless of other voters preferences. Strangely, this is a common conception of democracy we hold - the idea that "every vote should count" - yet as far as I can tell only the Insanity Voting method adheres to this principle. It seems as though Insanity Voting meets many, if not most, of the important Criteria for a good voting system. I recommend we implement it immediately for all official disputes. My vote counts, Scott Ritchie ---- Election-methods mailing list - see http://electorama.com/em for list info
