Thanks Ralph for pointing out my oversite. >> The primary may be non-monotonic as well as the general election but >> together they are monotonic.
>You presumably meant that the other way around. Plurality is >monotonic for both elections, but the 2 taken together result in >strategy and a non-monotonic effect? >Monotonic = voting for (or raising the preference of) a candidate >cannot result in that candidate losing SORRY, GOT IT BACKWARDS, MY FALUT. Let's Look at the example in wikipedia http://en.wikipedia.org/wiki/Monotonicity_criterion Number of votes 1st Preference 2nd Preference 39 Andrea, Belinda 35 Belinda, Cynthia 26 Cynthia, Andrea Using IRV "Cynthia is eliminated, thus transferring votes to Andrea, who is elected with a majority." In a primary Andrea and Belinda would be the top-two and would go to the general election. The Cynthia voters would now vote for Andrea in the general election (based on their preference). And the result would be the same as IRV. Let us now assume Cynthia voters manage to "...persuades ten of Belinda's supporters to change their votes to her at the next election." (or in this election) This election would look like this: Number of votes 1st Preference 2nd Preference 49 Andrea Belinda 25 Belinda Cynthia 26 Cynthia Andrea "Because of the votes Belinda loses, she is eliminated first this time, and her second preferences are transferred to Cynthia, who now wins 51 to 49." "In this case Andrea's preferential ranking increased between elections - more electors put her first - but this increase in support appears to have caused her to lose." "Counterintuitively, it was the increase in support for Andrea (along with the properties of IRV) that hurt her." They could use the same strategy in a primary. Belinda would be eliminated in the primary. Andrea and Cynthia would advance to the general election. Assuming that the Belinda voters preferences remain the same then Cynthia would win in the general election (51 to 49). The strategy worked in a IRV election and in a top-two election. It is clear that both voting SYSTEMS are non-monotonic. In actual voting (IRV or Top-two) there is very little chance that Belinda voters could be persuaded to vote for their third choice. In order for this strategy to work you would have to have a precise knowledge of all of the voters preferences (first and second). In this example if you missed the 2nd preference by 2 (say it was really - 23 Belinda Cynthia and 2 Belinda Andrea) Andrea would win (51 to 49). The 10 Belinda voters who switched would be very upset at the Cynthia voters who convinced them to switch, now they have to settle for their third choice, Andrea. The argument some people are making is that IRV has a potential flaw. Which I have pointed out, the top-two voting system has the same flaw. I also pointed out that the top-two has more of a chance of voter manipulation than IRV. It would seem that those opposed to strategic voting and voter manipulation are backing the wrong horse. All of this is not relevant. The only way it would be relevant is if an election method that is "non-monotonic" is unconstitutional. Which would rule out IRV and top-two. However, the U.S. Supreme Court has already ruled that the top-two is constitutional (see case below). It is the responsibility of the legislature (or the voters in this case) to decide on their election method, and it is the responsibility of the Supreme Court to decide if it is Constitutional. If you think that a voting method is flawed you need to take that issue to the legislature (or voters) who make the laws. If the law (a voting method passed by the people) is full of flaws and it passes the Equal Protection Clause (and other Constitutional issues) then the "will of the people" shall prevail. See Washington State Grange. v. Washington State Republican Party (2007) "...they threaten to short circuit the democratic process by preventing laws embodying the will of the people from being implemented consistent with the Constitution." Don Hoffard ---- Election-Methods mailing list - see http://electorama.com/em for list info
