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Better-Than-Expectation strategy, for Approval says to vote for every candidate who is better than<br>your expectation for the election.<br><br>The other Approval strategies are special cases of Better-Than-Expectation.<br><br>If you know who the frontrunners will be, and that the winner will be one of those two, one strategy<br>says to vote for the better of those two, and for everyone who is better than that.<br><br>But, if you know that the winner will be one of those two, then your expectation is somewhere between<br>the utilities of those two candidates, and so Better-Than-Expectation says to vote for the better frontrunner<br>and for everyone who is better.<br><br>Of course, strictly speaking, since your expectation has some specific value between the two frontrunners' utilities,<br>you should also vote for whatever other candidates are better than that inbetween point. So you aren't<br>just voting for the best frontrunner and everyone better--you're also voting for some candidates whose<br>merit is between those of the two frontrunners.<br><br>That's what is recommended in a Best-Frontrunner strategy suggested by Brams, Fishburn, or both.<br><br>As a practical matter, of course it isn't instrumentally important which, if any, inbetween candidates you vote for,<br>since you know that the winner will be one of the two frontrunners. But voting for a candidate shows<br>your support for that candidate, shows how many people like that candidate. That's why you certainly<br>want to vote for everyone better than the best frontrunner. And also for the inbetween candidates who<br>are better than that inbetween cutoff point that is your expectation, if you know where it is. But maybe you<br>only know who the frontrunners are; you might not have the information needed to find that inbetween<br>cutoff.<br><br>Now, suppose it's a u/a election (there are completely unacceptable candidates who could win).<br><br>The following isn't rigorous, but sounds compelling:<br><br>The unacceptables have arbitrarily immense negative magnitude for their utility, though they have<br>a finite probability of winning. That means that, inevitably, they pull your expectation below the<br>utilities of any of the acceptable candidates.<br><br>Similarly, because the acceptables are similarly immensely better than the unacceptables, and have<br>a finite chance of winning, they likewise pull your expectatation to better than any of the<br>unacceptables. So your expectation is somewhere between the utilities of the acceptables and<br>the unacceptables. Hence you should vote for all of the acceptables, and for none of the<br>unacceptables.<br><br>So, whether or not the election is u/a, and whichever of the abovementioned strategies you're using, <br>you're voting (only) for the Better-Than-Expectation candidates.<br><br>In a non u/a election, maybe you know who the frontrunners will be. But maybe not. But then,<br>maybe you still have a feel for how good you expect the election result to be, and so you<br>can judge which candidates are better than what you expect from the election.<br><br>You might want to ask yourself, regarding each candidate: Shall I appoint hir president, or shall<br>I conduct the election. If the answer is "Appoint hir president", then vote for hir.<br><br>Because, in all these strategies, you're voting for the Better-Than-Expectation candidates, then,<br>whichever of these strategies the various voters might be using, they're all voting for the<br>candidates better than what they expect for the election.<br><br>So the winner will be the candidate who is, for the most voters, better than what the voter expects<br>from the election. <br><br>The winner will be the candidate who maximizes the number of voters who are pleasantly-surprised<br>by the outcome.<br><br>Of course that's true in Score-Voting too, if voters are voting in their best interest, by giving maximum<br>rating to the candidates they'd vote for in Approval, and minimum points to the candidates they<br>wouldn't vote for in Approval.<br><br>The fact that Score-Voting affords that opportunity makes it one of the best voting systems.<br><br>There's a good chance that Score-Voting's great familiarity could make it the most winnable<br>voting system reform.<br><br>In fact, to propose Approval, you should first suggest Score-Voting, and then suggest the "Yes/No", <br>"Acceptable/Unacceptable", or "one point/zero points" version of Score-Voting--Score-Voting's<br>simplest version: Approval.<br><br>Introducing Approval as a Score-Voting version means that it benefits from the great familiarity<br>of being asked to cardinally rate things or people (from 1 to 10, for example). <br><br>And it avoids the erroneous criticism of Approval that claims that it violates "one-person-one-vote":<br><br>Approval, as a Score-Voting version, lets each voter rate each candidate (one point or zero points, yes or no).<br><br>Each voter equally only has one vote for rating any particular candidate.<br><br>No one could seriously try to claim that Score-Voting violates 1-person-1-vote.<br><br>Mike Ossipoff<br><br><br> </div></body>
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