[EM] contd, your method proposals

[Kevin Venzke]

Mike,

--- MIKE OSSIPOFF <nkklrp at hotmail.com> wrote:
> Kevin--
> 
> You said:
> 
> Since you advocate PC, which fails clone independence and SDSC, I don't mind
> selecting MinMax(pairwise opposition), which also fails those: Elect the 
> candidate
> for whom the greatest number of votes against him in a contest is the lowest
> such number among all candidates.
> 
> I reply:
> 
> Compared to PC, your method is indecisive, and more inclined to fail to 
> elect the CW.

I think it is worth it.

> Consider any standard wv truncation example:
> 
> 40: A (B>C preference truncated)
> 25: B
> 35: CB
> 
> Maybe you might want to consider your best proposal?

Do you mean "reconsider"? No, I am happy with the result in the above
scenario. Why on earth would the A voters truncate the B>C preference?
This causes C to obtain a great chance of winning when otherwise it is
a decisive B win.

> You continued:
> 
> I think the worst strategy problem is either the clear incentive to 
> equal-rank
> at the top, or the offensive order-reversal problem that WV methods also 
> have.
> 
> I reply:
> 
> Your method has a truncation  CW failure that PC doesn't have.

Well, the scenario above shows that if voters truncate the CW, they can
get someone they like less. That isn't your point, I'm sure.

> You continued:
> 
> In this scenario:
> 49 A
> 24 B(>C)
> 27 C(>B)
> 
> The result is a B-C tie, unless both B and C factions truncate, in which 
> case A wins.
> Break the tie by Random Ballot.
> 
> I reply:
> 
> Ok, that's interesting, and a good thing--That method halfway gets rid of 
> the defection problem without ATLO. But, with ATLO, wv deals with the 
> problem. And your method has a price (described above) for its halfway 
> solution of the problem without ATLO.

I don't understand why you say "halfway" if you're not referring to the
"price" of indecisiveness and poorer Condorcet efficiency.

In the three-candidate case, MinMax(PO) satisfies Later-no-harm and SDSC. In 
the above scenarios, it doesn't mess up IRV/Margins-style and it doesn't mess
up WV/Approval-style. Looks pretty perfect to me.

> You continue:
> 
> For a more sophisticated method, which satisfies clone independence and 
> SDSC,
> I suggest to declare a tie among all candidates who are not barred from 
> winning
> according to Markus' majority beatpath criterion. (I refer to this method as
> "CDTT,RB.")
> 
> I reply:
> 
> The public doesn't like indecisiveness. Why don't you just propose 
> BeatpathWinner instead?

Well, for greater decisiveness, you can preserve clone independence,
monotonicity, and 3-candidate LNHarm by electing the non-barred candidate who is 
ranked the highest using Woodall's DSC method. But I find that this gives
less intuitive results. It means that on the 49 24 27 ballots, C wins with
100% probability.

I don't propose BP in this case because part of the point of CDTT,RB is to
address the defection problem. When only majority-strength defeats are
regarded, then adding a preference can create a defeat, but it can't reverse
the direction of one. That means voters don't need to worry that adding a
new preference could turn that candidate into the CW (who would automatically
have to win, in a Condorcet method).

> But either BeatpathWinner or CDTT,RB is a good method, if people don't mind 
> CDTT,RB's indecisiveness.

I'm happy you think so.

A big reason I don't mind the indecisiveness, is that the voters have the
power to avoid indecision: They can vote non-cyclic majority-strength wins.

The second reason is that I don't want to discourage candidates from running.
Electing B instead of C in the above scenarios (when B voters truncate) is a 
"safer guess" to be sure, but it's just a guess. Since C can be elected without
violating majority rule, it could be seen as drastic to completely rule C out,
and a great disincentive against C entering the race.

> By the way, though someone has probably already mentioned this, the immune 
> set, the set of candidates who could be elected without violating the Strong 
> Beatpath Criterion (SBC) is the same as the winner set of BeatpathWinner. 
> SBC is based on Steve's BC.

Maybe I should note that I want to use Markus' BC with Random Ballot, because 
using Steve's BC is not monotonic. I can give an example if desired.

Kevin Venzke



	

	
		
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