[EM] Lotteries and random numbers

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
> We need provision for breaking ties.  I offer a thought that avoids 
> tossing coins:
>      If counts are even, give candidate with lower name an extra vote.
>      If counts are odd, give candidate with higher name an extra vote.
> 
> Big deal is I am an enemy of lotteries in voting:
>      Hard to come up with a formula for conducting the lottery.
>      Hard to prove the formula has been obeyed - cheating in the 
> counting is obviously tempting.
> 
> Some methods of voting can inspire extra temptation for strategizing - 
> and temptation to try to counteract suspected strategizing.  Avoiding 
> such voting methods may be the most practical way to avoid the problem.
> 
> Some supposed strategizing assumes shared knowledge and plotting that 
> does not deserve attempts to counteract because the supposed sharing of 
> knowledge and planning is not practical in real elections.

Another option is this: use the total count as the seed for a good 
pseudorandom number generator. True, it can be tricked by simply 
calculating (add write-in ballots until it goes one's way), but if the 
adversary has power to disturb the counts so that it sums to a 
particular value, your method won't work either.

Your method can in any event be generalized: if there's an n-way tie, 
order the candidates from 0 to n exclusive in alphabetical order, then 
calculate x = (total mod n). Count up to x (first is zero), and that 
candidate gets an extra vote. There may be some (weak) statistical 
problems if one can guess the range of total - something about how some 
digits will appear slightly more often than others - if that breaks the 
scheme, use a PRNG or hash.