[EM] Responses to some of Forest's ideas

[Rob LeGrand]

Forest wrote:
> 3. It eliminates the occasional low utility Condorcet Winner.

I question the advantage of this . . . advantage.  ("Allow myself to introduce
. . . myself.")

> My main disagreement with Demorep is that I tend to prefer the Approval
> winner over the majority first place winner in the rare instances when the
> two might differ. But I'm sure that the public would side with Demorep on
> this issue.
>
> Example:
>
> 55 A > B >> C
> 45 C > B >> A
>
> Demorep and most other people would say that A is the clear choice of the
> people. The 45% minority lost the election fair and square. Let them tough
> it out for the next four years.
>
> I believe that B would be more likely to represent the common interests of
> the people.

I agree with the last statement, but I still think A should be elected.  Unless
sincere votes can be assumed, any ranked-ballot election method should always
elect a voted Condorcet winner; otherwise, the sincere Condorcet winner will
tend to be elected anyway through strategy.  In the above example, electing B
over A would encourage the A voters not to approve B.  The best election
methods make it very unlikely that an individual voter will regret his ballot
choice(s) after the results are announced.

Earlier, Forest wrote:
> Since Borda (according to Rob LeGrand's simulations, for example) has
> significantly higher expected social utility than any of the Condorcet
> methods, we can be confident that Borda Seeded Single Elimination and
> Borda Seeded Bubble Sort will be near maximal with respect to expected
> social utility among methods that satisfy the Condorcet Criterion.

Further simulations have shown that BSSE indeed has a high expected social
utility given sincere votes, but surprisingly it doesn't seem to be the SU
champ of Condorcet methods.  The best one I've found is what I call Borda(wv):

1. Calculate the pairwise matrix.
2. For each entry Pij, set it to zero if it's less than Pji (this is the step
   that makes it different from Borda).
3. Calculate a score for each candidate by subtracting its column sum from its
   row sum.
4. Pick the candidate with the highest score.

My simulations haven't found an example for which Borda(wv) fails to choose the
Condorcet winner, or even within the Smith set, and I haven't been able to
construct a contrived example.  Can anyone show that Borda(wv) is or isn't a
Condorcet method?  I don't expect Borda(wv) to have as many desirable
properties as the best Condorcet methods, though.

--
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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