A proportionally fair lottery is a lottery method in a which any faction of the voters can unilaterally guarantee that their common favorite will be elected with a probability proportional to the size of their faction.
A consensus candidate is any candidate that would be liked at least as much as the random favorite by 100 percent of the voters (assuming all voters to be rational). A consensus lottery is a method that elects consensus candidates with certainty (again, assuming rational voters). I won't attempt to define "sincere range ballot" here, but the meaning will be apparent from this method: Ballots are range style (i.e. cardinal ratings). Each voter rates the candidates, circles one of the names as a proposed consensus candidate, and labels another (or perhaps the same) name as "favorite" or "favourite." Have I overlooked anything? The ballots are collected and the probabilities in the "random favorite" lottery are determined. These probabilities are used to determine and mark a "random favorite rating expectation" on each range ballot. A ballot is then drawn at random. If the circled name on the randomly drawn ballot has a rating above the "random favorite rating expectation," on any ballot (including the one in play), then another ballot is drawn, and the indicated favorite of the second ballot is elected. Otherwise, the proposed consensus candidate whose name was circled on the first drawn ballot is elected. That's it. Note that any voter has the power to turn the election into "random favorite" by giving only one candidate (favorite=consensus) a positive non-zero rating. But whenever that is optimal rational strategy, sincere range yields the same expectation, and is therefore optimal, too. ---- Election-Methods mailing list - see http://electorama.com/em for list info