2013/6/12 Richard Fobes <electionmeth...@votefair.org> > On 6/12/2013 7:55 AM, Jameson Quinn wrote: > >> >> ... (As far as I know, MJ can only be expressed in one >> way). ... >> > > I wrote the following brief description of Majority Judgment. Is this > correct? If so, perhaps it's useful? > > "Starting with any candidate, count the number of voters who give this > candidate the lowest score. If the count is more than half the voters, > then the candidate is given this score. If the count is less than half > the voters, the number of voters who assign the next-higher score is added, > and the process is repeated until the count exceeds half the voters. > Repeat this process to identify each candidate's 'median' score. > Whichever candidate has the highest median score is the winner. > Frequently two or more candidates have the same median score, so the tie is > broken by removing ballots one at a time as needed, where the removed > ballots are the ones that assign the same median score to the tied > candidates." >
Right, that's a good description of MJ. And my point was, any description of MJ will use essentially those same words, or equivalent ones, for the tiebreaker. On the other hand, GMJ can be described without a separate tiebreaker step, in three separate ways: 1. Count the votes at the highest grade for each candidate. If any one candidate has a majority, they win. If not, add in lower grades, one at a time, until some candidate or candidates get a majority. If two candidates would reach a majority at the same grade level, add the votes at that level in a graduated manner; that is, first add 10% of all votes at that grade to each candidate, then 20%, stopping when exactly one candidate has reached a majority; that candidate wins. For the purposes of reporting results, a candidate's score is the grade level they reached a majority at, plus one half, minus the fraction of the votes at that level which it took to reach a majority. (This is the same number as the formula below gives.) 2. Calculate (median + (V> - V<) / (V= * 2)) for each candidate. The highest score wins. V>, V<, and V= represent the number of votes above, below, and at the median, respectively. (If V= is zero, then (V> - V<) will also be zero by the definition of "median", so in that case you can assume that V= is 1, or any other non-zero number, to avoid division-by-zero problems.) 3. For each candidate, graph the cumulative grade distribution using rectangles for each grade that meet at the corners. Draw a single line that goes diagonally across each of the rectangles. The candidate who's line is highest at the 50% mark is the winner. (This explanation makes more sense if you see an example). Note that all of these descriptions do essentially the same thing whether or not there's a tie. In description one there's an aspect of "go back and do it slowly", but not "try something completely different" as with MJ. Jameson > (I'm aware that the description does not specify which score is used if > the median lands on a transition point. The purpose of this description is > just to introduce the general concept.) > > Richard Fobes > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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