[EM] Best Deterministic Ranked Preference Method?

[Kevin Venzke]

Hi Forest, two replies in one:

>On Wednesday, December 23, 2020, Kevin Venzke <stepjak at yahoo.fr> wrote:
>>
>> I thought it was odd that if one votes A>B (approving both) and B pairwise defeats A, then A can't get credit for this 
>>vote. So I took the liberty of devising another method called BTP (P=preferred). In BTP, instead of checking for losses 
>>to all the approved candidates, you check for losses to the candidates strictly preferred to the candidate you're 
>>scoring. This revised method turns out to be incredibly similar to MinMax(WV). It's not so obvious to me yet why it 
>>should be, but for now I'm amazed.
>>
>We're getting close with BTP!
>
>My tweak: x gets a point from every ballot B on which it is both ranked AND it pairwise beats every alternative 
>ranked strictly above it on that ballot B.
>
>More generally, ... a point from every ballot on which it is both approved and it beats every alternative ranked above it.
>
>(No alternative gets a point from any ballot on which it is not approved, i.e. not ranked in the case of implicit approval)
>
>How about that?

I call this BTPA. (But I used beat-or-tie, not strictly beat.) It is quite different from BTP or BTA, and appears extremely similar to Condorcet//DSC, especially with 3 candidates. For my taste this is not very good. It's also pretty close to fpA-fpC though, with 3 candidates.

Basically with BTPA your score as a candidate is capped by your implicit approval, and you can be deprived of it by weaker candidates who beat you pairwise. In contrast it seems to be important to BTP's properties that candidates can score off of ballots that didn't vote for them, which only voted for candidates that were beaten by them.

Also, it seems to me to be an advantage of BTP over BTA or BTPA that you don't need any implicit approval concept.

---

Regarding HBH and Weinstein, I'm having a lot of trouble getting this to work reasonably. For one thing, I can't find a way to interpret single-round Weinstein DSV Approval so that it is monotone. Also, if approval can extend into the bottom rank, it violates Plurality a lot. I can disallow that, but this creates a lot more monotonicity issues.

(One could suggest that the approval cutoff be placed prior to the rank that exceeds 50% of the random ballot odds, but this doesn't seem workable because it means a majority favorite can't receive his votes.)

Here's a Weinstein mono-raise example for your consideration.

0.311: D>C>A>B approves DCA
0.270: A>B>C>D approves AB
0.186: C>B>D>A approves CBD
0.143: B>D>A=C approves BD
0.087: B>D>A=C approves BD

D wins. Now change the 0.143 bloc to vote D>B at the top instead of B>D. I find that this causes the .311 bloc to stop approving A (since D carries more weight now), and the .270 bloc to start approving C (since B carries less weight). So now C wins.

Kevin