[EM] average voting power and block votes

[Richard Moore]

Forest Simmons wrote:

> 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


Excellent work! That's more in line with what I was thinking 
about. In this case, we see that with the block voting 
arrangement the voters are giving up some of their power to 
an arbitrary factor. This arbitrariness can easily be seen 
this way: Suppose the vote is held before the blocks are 
designated, and the result is 5 to 4. Now divide the voters 
into blocks by lottery. Every now and then you will get a 
distribution like 3-0, 1-2, 1-2, which gives a result that 
contradicts the popular vote. So some voting power is 
surrendered to randomness, and (statistically) no voter 
gained any power as a result of that sacrifice.

Richard