[EM] average voting power and block votes

[Forest Simmons]

On Wed, 25 Jul 2001, Forest Simmons wrote:

> 
> I hope the example of three subcommittees of three members each can serve
> as a test case for any new definition of voting power.
> 
> Here's an experiment that might help:
> 
> Simulate both the three blocks of three and the one group of nine systems. 
> In both simulations keep track of how many times the winner agrees with
> the choice of the first (or randomly chosen) voter. 
> 
> If the individual voters have any real power, the long range number of
> agreements should exceed the long range number of disagreements.  If the
> block system produces significantly more agreements than the non-block
> system, then that would constitute evidence that the block system
> increased individual voting power, and tell us that Banzhaf Power is
> obsolete in this context. 
> 
> I suspect that the non-block voter has an advantage in this experiment,
> but perhaps not as large as the 35 to 32 advantage that the Banzhaf Power
> indices would have us believe, since the experiment counts agreement and
> disagreement in all cases, pivotal or not.
> 

According to my calculations the long range results of these simulations
should be ...

in the block vote case, the random voter would agree with the final
outcome 62.5 percent of the time.

in the "popular vote" case, the agreement is improved by a fraction of
3/256 .

The ratio of agreement in the second case to the first case is 163/160.

The "popular vote" is more responsive to the voter.

In other words, the conditional probability of the "popular vote" yielding
a yes outcome, given that a randomly chosen voter voted yes, is greater
than the conditional probability of the block vote system yielding yes,
given that a randomly chosen voter voted yes.

[And the same holds true if "yes" is replaced with "no".]

Forest