--- Scott Ritchie <[EMAIL PROTECTED]> wrote: > This definition bothers me a bit. We tend to think of "sincere" > votes as non-strategic, but the method you just described for > "voting sincerely" can involve a whole lot of strategy based around > resizing the sets and setting the approval threshold.
It is important to recognize that sincere and non-strategic are different concepts which may intermingle differently in different situations. It is also important to recognize that there is nothing inherit in sincerity that requires an election method to have a unique sincere vote for each voter. When a voter has multiple sincere votes for an election method, tactics can be a factor in which of those sincere votes are actually cast. I describe a sincere vote as one which reflects as accurately as possible the person's personal preferences. The preferences are ones that are independent of the election method, independent of information about how other voters will vote, and independent of the addition of another candidate. Reflecting those preferences as accurately as possible is judged relative to the voting limitations imposed by the election method and to an overall design intent or other normative specification for voting with the election method. For ranked ballot election methods, except for maybe issues about how ties in preferences are handled if ties are not allowed in the voted rankings, there is a unique sincere vote. Similarly for plurality voting. For approval voting, the issue depends or whether you think people have an approval preference that is independent of adding an additional candidate. If so, each voter has a unique sincere vote. If not (and I don't), then there are multiple sincere approval votes, depending on where an approval threshold is applied. Assume a voter has preferences that can be represented by a von-Neumann-Morganstern utility function. For range voting with infinite precision, there are infinite sincere votes: those that preserve the relative differences in preference strength between the options. Distorting the relative differences between preferences by pushing middle options disproportionately towards the extremes is not a sincere range vote. In discrete range voting, some details can get messier about how to deal with rounding issues. Multiple sincere votes are still possible though. In discrete range voting with just two rating options, the threshhold has to be set at the average of the max and min preferences. That means a vote could be a sincere approval vote but not a sincere range vote. That is not a contradiction, just a result of (what I see as) the different design intent / normative specification for range vs. approval voting. I'll claim that for election methods which allow a voter to have multiple sincere votes, the only way for such a voter to vote purely sincerely is for that voter to randomly select, using a uniform distribution, which sincere vote to cast. -- David Cary ____________________________________________________________________________________ Expecting? Get great news right away with email Auto-Check. Try the Yahoo! Mail Beta. http://advision.webevents.yahoo.com/mailbeta/newmail_tools.html ---- election-methods mailing list - see http://electorama.com/em for list info
