[EM] Viability (finding the odds after you've voted)

[Forest Simmons]

Thanks for the suggestions.

I'm open to new ideas for measuring candidate viability at the various
stages, but I am wary of methods that use probabilities to compute
expectations, because it is very tricky to pin down the precise
probabilities that some candidate will eventually win.

That's the main reason I adopted the "wait and see" creative
procrastination strategy.

If the viabilities roughly correspond in order (though not necessarily
strictly proportional in magnitude) to the probabilities of winning, then
one can safely choose one merger on each ballot, procrastinating the
remaining mergers until the viabilities are known more precisely.

I'm confident that the new rule for using the viabilities would be
precisely right if we knew the exact order of the probabilities, without
knowing the probabilities themselves.

For example, it doesn't matter if the probability lineup on a ballot is

20%, 65%, 15% or
35%, 40%, 25% .

The viabilities could be  2,3,1  or  5,6,2  or  4,9,2.

The mergers are the same, the second and third slots merge.

This robustness is appealing to me for the following reason:

If the voters can estimate the viabilities of the candidates on the basis
of imperfect polls, then they can order the n candidates on a three slot
ballot well enough for the robustness to give the right result, making up
for the deficiencies of the polls.

And we know that we have the right rule for the three slot ballot!

So in the case of the Three Slot Max Power Cardinal Rating method, we
could justly claim the name MVP, the "Max Voting Power" method.

Note how this corresponds with the technical definition of voting power,
the probability of your vote being pivotal.

Forest




 On Fri, 1 Aug 2003, [iso-8859-1] Kevin Venzke wrote:

> I have a decent idea for a refinement, which might permit CR to boil down
> to Approval ballots filled out per the Better-Than-Expectation strategy.
> You could also do the Maximum Power strategy.
>
> Suppose there are two factions that vote roughly as follows:
> 50%: A 10, others 0
> 50%: B 10, C 10, others 0
>
> If you use the normal viability definition (Borda score, or CR sum), it looks
> like the candidates have an equal chance of winning.  But intuitively this is
> not so.  A has a 50% chance of winning, and B and C each have about a 25%
> chance.  The math to produce these odds is pretty simple:
>
> Instead of giving a candidate the score it was given from a certain ballot, give
> it the score AS A PERCENTAGE of the total points awarded from that ballot.  (That
> means total points awarded from a ballot equal 1.0, regardless of how many slots
> were on that ballot.)
>
> Now that the score is measured with more sophistication, we can actually guess
> at each candidates' odds of winning.  No need to worry about front-runners.
>
> Let me attempt an example.
>
> 50: A 10, E 3
> 50: B 10, C 10, D 10, E 6
>
> A gets (10/13)*50 or 38.46% odds
> B C and D each get (10/36)*50 or 13.88% odds
> E gets (3/13)*50 plus (6/36)*50 or 19.87% odds
>
> Odds total 100% (or should).
>
> First faction's expectation:
> 10*38.46% + 3*19.87% = 3.846 + .5961 = 4.4421
> Second faction's expectation:
> 3(10*13.88%) + 6*19.87% = 4.164 + 1.1922 = 6.086
>
> Resulting approval ballots:
> 50: A
> 50: BCD
>
> I do find it slightly bizarre that E gets "more odds" from the first faction
> than the second.
>
>
> For the Maximum Power strategy:
> Instead of calculating expectation, you try to approve candidates with a total
> of 50% odds.
>
> First faction:
> A alone is 38.46 (11.54 from 50), A and E is 58.33 (8.33 away).
> Second faction:
> BCD sum to 41.64 (8.36 off); adding in E gives 61.51 (11.51 off).
>
> So the result is the same, except that the first faction also approves E.
>
> Any thoughts?
>
>
> Kevin Venzke
> stepjak at yahoo.fr
>
>
> ___________________________________________________________
> Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français !
> Yahoo! Mail : http://fr.mail.yahoo.com
> ----
> Election-methods mailing list - see http://electorama.com/em for list info
>