[EM] Cumulative Vote equivalence to Plurality

[Brian Olson]

Catching up on something from a few days ago.

On May 29, 2004, at 4:07 PM, Bart Ingles wrote:

> Forest Simmons wrote:
>>
>> Someone (Kevin or Bart or both) recently reminded us that the usual
>> version of Cumulative Voting is strategically equivalent to Plurality.
>>
>> However the recent proposal allowing both positive and negative votes 
>> with
>> the sum of absolute values limited, is different: it turns out to be
>> strategically equivalent to a method that (like plurality) allows 
>> only one
>> mark, but that mark can be either positive or negative, i.e. you can 
>> vote
>> for a candidate or against a candidate, but not both.
>
> Ahh, I see that now.  I think someone had pointed this out earlier, but
> I wasn't following closely enough at the time.
>
> In that case, given the sincere ratings of:
> A(1.0) > B(.99) > C(.98) > D(.97) > E(0)
>
> my IRNR ballot would be something equivalent like:
> A(0) > B(-.001) > C(-.000001) > D(-.000000001) > E(-1.0)

I think you got your negative numbers off and meant
A(0), B(-0.000001), C(-0.0001), D(-.01), E(-1.0)

> The idea is the same, to choose values which keep the bulk if my voting
> power focused on a single choice regardless of elimination order.
>
> So ratings still aren't necessary for optimal strategy; you could just
> rank the candidates but allow the value of each vote to be positive or
> negative.  Thus:
> E(neg) > A(pos) > B(pos) > C(pos) > D(don't care)
>
> I concede that this method may be an improvement over IRV (which isn't
> saying much), but probably suffers from most or all of the same
> theoretical defects.
>
> Bart

If you choose to vote with an exponential difference between your 
ratings, then _for you_ IRNR is equivalent to IRV. Your ballot becomes 
equivalent to a single positive/negative vote at each stage of the 
process. Other voters are not so constrained.

I don't know what the _best_ strategy for IRNR is. I hope that it is to 
cast an honest ballot.

I define my criterion for 'best strategy' probabilistically. The best 
strategy is the one that is most likely to get you what you want. I 
suppose that does leave open the possibility of oddities in some 
scenarios.

If we find more than one election method which has a best strategy of 
voting honestly, then the best method is the one which satisfies the 
utilitarian goal of being the most likely to make the most people the 
happiest. That's where I'm going with my simulations. I just need to 
add a bit more complexity on the strategy side.

Brian Olson
http://bolson.org/