[EM] Venzke's election simulations

[Kevin Venzke]

Hi Warren,

--- En date de : Mar 8.6.10, Warren Smith <warren.wds at gmail.com> a écrit :
> comments by WDS
> 
> 1. I think using utility=-distance
> is not as realistic as something like
> utility=1/sqrt(1+distance^2)
>
> I claim the latter is more realistic both near 0 distance
> and near
> infinite distance.

Why would that be? Do you mean it's more intuitive?

> 2. It has been argued that L2 distance may not be as
> realistic as L1 distance.
> L2=euclidean
> L1=taxicab

That's interesting. I wonder what arguments were used.

> 3. Your "candidates bolted in place" (in locations selected
> manually)
> at some point needs to be replaced by an outer loop which
> chooses
> their locations from some distribution, and finds average
> bayesian
> regret over all candidate locations.
> If I manually choose locations, I can probably make nearly
> any method look like
> "the best" or "worst" method...   that is
> kind of anecdotal evidence
> versus real evidence.
> (Not that the anecdotes are uninteresting.)

Well, it would be better to cycle over some of the locations, but taking
the average over all possible locations would not be very good evidence
either, since not all locations are equally likely.

On the other hand if you select a scenario that seems likely to occur
in practice, I think that is good and useful evidence, especially if you
can't refute your conclusion by changing the scenario slightly.

If you stick to reasonably realistic scenarios I really doubt you could
find a way to make any method you like best or worst.

> 4. your results look interesting but I do not know what a
> lot of your
> voting methods are, e.g. QR, VFA, SPST, C//A, etc. 
> Too abbreviated.
> Need to supply a key.

Of these:
C//A: Elect the CW if extant, else the Approval winner. 
(Condorcet//Approval)
VFA: This is what you have called Venzke Disqualified Plurality.
Elect the FPP winner except that when more than half of the voters 
rank this candidate strictly last, instead elect the second-place FPP
candidate.
SPST: This is the same as VFA except that when the FPP winner is 
disqualified, his supporters' preferences are transferred, instead of
simply electing the second-place candidate.
QR: This is a new method by me called Quick Runoff. Elect the candidate
with the most first preferences who does not have a full majority pairwise
loss to the very next candidate in first-preference order.

There is also CdlA (Conditional Approval) which is a method where voters
gradually add more of their preferences as a result of disliked options
being the vote leader in a "round."

> 5. some conclusions, like RangeNS is better than IRV and
> IRV-tr and C//A, look
> fairly solid (happen in all your sims*); others, like
> Bucklin is
> better than RangeNS,
> look inconclusive (happen in some of your sims, but reverse
> happens in
> other sims)
> 
> *There was one exception, but it had very small regret for
> all methods
> other than MMPO and ApprZIS.

I don't try to draw many conclusions at this point simply because not
many scenarios have been analyzed. I mean four of the scenarios I posted
were only 1D. And most of the utility differences were very small.

Kevin Venzke