## Some Simple Computer Simulations of Iowa 2008

### How often do the Range Voting and Approval Voting winners differ?

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.

### How often do the Range Voting and Approval Voting winners differ from the Plurality winner?

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.