While I was working on my "Crosscut" method of voting, I realized early on that I needed a way of dealing with truncated ballots. If I simply ranked all truncated candidates in last place, I would be encouraging people to truncate everyone but their top choice, which kind of defeats the purpose of rank voting. At first I handled truncated ballots as if they were "tied" ballots. In other words, if there were candidates A, B, C, X, Y, Z, and someone only voted ABC, then X would receive 1/3 of a vote for fourth place, 1/3 of a vote for fifth place, and 1/3 of a vote for sixth place; the same for Y and Z. This doesn't encourage truncated ballots, but doesn't really discourage it either. I then realized that if I assumed that truncated ballots indicate no preference rather than identical preference, I could re-order the truncated ballots so the electorate as a whole was slightly happier without lowering the happiness of the voter who truncated his or her ballot. As an analogy, if I disliked the colors beige, almond, and cream equally -- or if they all looked the same to me -- allowing someone to choose almond over beige and beige over cream would make him or her happier without harming me. To use the ballot above, if one person voted ABC and another voted AXBYCZ, then turning the truncated part of the first vote to XYZ -- in effect making his vote ABCXYZ -- would improve the overall satisfaction of the electorate. The same can be done with tie votes. Say that instead of truncating my ballot I voted ABC(XYZ tie). Let's assume that the rest of the electorate has the following combined rankings for the XYZ triplet: order XYZ: 35% order YZX: 25% order ZXY: 40% We would then have the adjusted rank of ABC (X35, Y25, Z40)(X40, Y35, Z25)(X25, Y40, Z35) where each set of parenthesis encloses a rank, and the numbers indicate the percentage of the rank for each candidate. We could go even further and have the winner of (XYZ) in the remaining electorate have sole possession of the first available rank, the #2 candidate in (XYZ) the second available rank, and the last one the remaining rank. This has the added benefit of only handling "whole" votes. In the vast majority of single-seat elections this truncation/tie method will have very little influence, but in multi-seat elections it might help increase the overall happiness of the electorate by electing someone who would otherwise be narrowly defeated. The cool thing about this is this gives a positive incentive to vote for every rank if you have *any* preference at all: not only does it prevent an order of candidates you don't like, but it gives you a bit more influence if someone *else* does not fill out his or her ballot. If you *really* have no preference between two candidates, you can tie or truncate however you want -- you don't have to fill out the ballot randomly for your remaining votes to be counted. On the other hand, if you want to put a hated rival to your favorite candidate at the bottom of your ballot "strategically" or sincerely, it is in your best interest to rank every candidate in between. Of course with my method this would have to be recalculated after every pass, but computer time is cheap and this would add (marginally of course) to the overall happiness of the electorate. In addition, if those truncated or tied formed a circular tie, you could use a Condorcet completion method to choose a rank order to put into the list. Mike Rouse [EMAIL PROTECTED]
