We consider a maximally simple model in which each voter regards each of the C candidates as having a random number as his election utility. There are V voters, and a percentage F of them are "strategic" with the rest honest. On this page, by "strategic range voter" we mean "honest approval voter using threshholding based on the mean candidate utility." Thus with F=100 Range and Approval act identically. The results of running the program are:
C V F %where winner differs #elections simulated -- --- --- --------------------- -------------------- 10 101 100 0 65536 10 101 50 32.6 65536 10 101 0 40.6 65536 10 100001 50 30.9 256 * 10 100001 0 35.5 256 3 101 50 19.6 65536 3 101 0 23.4 65536 3 100001 50 23.0 256 3 100001 0 23.4 256
The line with the "*" is the closest approximation to Iowa 2008 situation. As you can see, the Approval Voting and Range Voting winners differed in 31% of those simulations.
We again consider the maximally simple model in which each voter regards each of the C candidates as having a random number as his election utility. There are V voters, and a percentage F of them are "strategic" with the rest honest. On this page, by "strategic range voter" we mean "honest approval voter using threshholding based on the mean candidate utility" and by "strategic plurality voter" we mean "always votes for one of the first two candidates, whichever has greater utility." The results of running the program are:
C V F %where winner differs #elections simulated -- --- --- --------------------- -------------------- 10 101 100 90.0 65536 10 101 50 83.3 65536 10 101 0 69.1 65536 10 100001 100 84 256 * 10 100001 50 86 256 * 10 100001 0 75 256 3 101 100 43.1 65536 3 101 50 46.4 65536 3 101 0 32.2 65536 3 100001 100 40 256 3 100001 50 48 256 3 100001 0 37.6 256
The lines with the "*" are the closest approximations to Iowa 2008 caucus situation.
At least in this model it is clear that the chances of a visibly different result in Iowa 2008 from adopting range instead of plurality, are large, and if both the Dem and Repub primaries are considered, the probability that a winner will differ in at least one of the two party's cases, is very large.