[EM] Re: Testing 1 2 3

Bart Ingles bartman at netgate.net
Sun Jan 4 12:12:01 PST 2004

Dgamble997 at aol.com wrote:
> Bart Ingles wrote:
> >But truncation is equivalent to equal last-choice preference for all of
> >the methods listed below.
> Yes, it is equivalent but expressing an equal preference for two or
> more candidates is generally considered as different to not ranking
> candidates you don't like.

I don't understand this.  How can it be both equivalent and different? 
I guess I don't understand the distinction you are making here.

> >Good strategy requires either utilities or strategic info, or
> >preferably both.  Although I suppose you could assume pure strategy if
> >you also assume that each voter knows how all the other will vote. In
> >that case approval should be essentially equivalent to Condorcet.
> Please explain further, with 3 candidates Approval strategy comes down
> to either approving one candidate (your first choice) or two ( your
> first and second choice).

In the hypothetical situation where a voter has complete data on other
voters' preference orders, best approval strategy is generally (when a
Condorcet winner exists) to vote for the Condorcet winner plus anyone
you like better, but omit the CW if a preferred candidate would be the
approval runner-up.  This always results in either 1 or 2 approvals in a
3-way race, and would generally elect the Condorcet winner if there is
one (except in tie situations).

With anything less than perfect info, best strategy requires the voter
to balance utility against uncertainty.  With 3 candidates, always vote
for your favorite, never for your least favorite, and vote for the
middle candidate if his utility is higher than the utility of the
expected outcome of a race between the other two (with zero-info, this
is simply the average utility of your most- and least-favorite
candidates).  This also results in 1 or 2 approvals, but may not agree
with the perfect-info strategy.

In a realistic scenario, it's inconceivable that individual voters (even
hypothetical ones) would know their own preference orders, yet fail to
know their own utility levels for each candidate.  It's also
inconceivable that perfect strategy info would be available.  Thus the
voters would generally base their strategy at least in part on utility.

Since we don't know how the voters would rate the candidates, but have
to assume the voters themselves know, it seems reasonable to assume a
range of opinions with half the voters rating their middle candidate
above average, and half below average.  Thus in the zero-info case, I
would expect to see half the voters approve exactly one candidate, and
the other half to approve exactly two candidates.  It turns out that
this gives results identical to Borda.

To simulate partial-info cases, you could probably use a weighted
combination of perfect-info strategy and zero-info strategy (but I
wouldn't expect accuracy on the level of more elaborate models, e.g.

> >> In strategic voting whether A>B voters approve A or A and B
> >> depends on how the voters respond to the information in an opinion
> >> poll using strategy A. In non-strategic voting the voters approve
> all
> >> candidates they like and hence A>B voters approve both A and B.
> >Again, this last assumption either invalidates the approval results
> or
> >the ranked ballot results (or both).  If you assume that the voters
> >truncate all preferences that they wouldn't approve of under approval
> >voting, then you are altering the ranked system results.  If, on the
> >other hand, you assume that the voters only truncate when they
> sincerely
> >don't have a preference between the truncated candidates, then your
> >approval results are invalid.
> Any assumptions made in the model are clearly stated in the
> instructions.

That may be, but from what you describe there is no way to derive a fair
comparison between the different methods.  For example, how do you
represent voters who think that their 2nd choice is much worse than
average?  To give accurate approval results, as I understand your model,
you can only have them rank one candidate.  But this requires them to
truncate under Condorcet or IRV, which would rarely be ideal strategy
for those methods.  So in order to give an accurate portrayal of
approval voting, you need to give an inaccurate picture of the ranked
methods, and vice-versa.

> You appear to be criticising the model on a lack of information. I
> will happily send you one if you want.

I'd be happy to look at it.


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