[EM] Strategic Bucklin variant?

Wed Dec 16 22:57:59 PST 2020

Hi Etjon,

I'll call your method EBBV. At first glance it seemed to be the kind of method where voters adjust their approval voting strategy after considering the current apparent outcome. But it's actually different from that, because the voters are required to move their thresholds towards finding and accepting the apparent compromise choice. I don't think I have previously seen a method where approval can be granted and taken back and yet the process reaches a natural conclusion.

When it comes to splitting the difference between Bucklin and IRV, it seems like you did a great job. It's about equally dissimilar to both.

Similarity to selected methods, with 3 cands 4 blocs, 4 cands 5 blocs, and 4 cands 4 blocs allowing ER:
EBBV-VBV: 0.997 0.850 0.782
EBBV-NWL: 0.981 0.857 0.836
EBBV-IBIFA: 0.972 0.890 0.790
EBBV-C//A: 0.949 0.851 0.864
EBBV-CdlA: 0.941 0.849 0.866
EBBV-DAC: 0.938 0.810 0.770
EBBV-INE2: 0.933 0.826 n/a
EBBV-MinMaxWV: 0.928 0.873 0.857
EBBV-AER: 0.927 0.845 n/a
EBBV-DMC: 0.927 0.865 0.878
EBBV-DiamA: 0.919 0.848 0.862
EBBV-Bucklin: 0.888 0.773 0.758
EBBV-IRV: 0.882 0.757 n/a
EBBV-INE1: 0.882 0.770 n/a

With 3 candidates it's very similar to my own Bucklin variant (VBV), but mine is effectively a three-slot method, so the similarity goes away with more candidates. With 4 candidates (and no ER), EBBV was closest to Chris Benham's IBIFA. With ER, it was closest to DMC, a Condorcet rule using approval.

Brief method key: In NWL (No Worse Losses) the winner is either the top rank winner or the implicit approval winner. Condorcet//Approval is maybe clear. CdlA (Conditional Approval) is a method of mine that has some similarity in form to EBBV, although approval once granted can never be taken back. DAC is Woodall's unusual method that plots near Bucklin. "INE" methods are two ways of doing IRV without eliminations. AER is approval-elimination (instant) runoff. And DiamA is one of Forest's recent diameter methods, using approval.

Regarding properties. One noteworthy thing is that both Bucklin and IRV satisfy Later-no-help, while EBBV gives that up. It doesn't fail it too badly though.

For Condorcet efficiency, I found Bucklin consistently the worst of the three. With 3c 4blocs, I found IRV slightly better than EBBV. With 4c 5b IRV was slightly worse.

For LNHarm, EBBV is far better than Bucklin (with 3 candidates, 20.5% bad scenarios vs. 6.6%), and is competitive with the methods it is similar to (VBV, IBIFA, NWL), but other methods do better (AER, DMC, WV, CdlA, and C//A range 1.6% to 4.4%).

For Mono-raise, EBBV seemed about the same as IRV... This could be off though. I don't seem to find many Mono-raise issues in general. It's at least pretty obvious to me that a method like EBBV would not be monotone.

I have a Compromise metric aside from FBC. It's just about dropping one's favorite to equal last in attempt to improve the result. By this metric Bucklin is not actually a very good method. But IRV is one of the worst. EBBV was slightly worse than Bucklin, except with the ER scenario, where for some reason it was considerably better.

For FBC, we can use only the ER scenario where IRV is excluded. Bucklin(ERW) satisfies FBC fully. I found EBBV not bad but not amazing, about the same as Condorcet//Approval.

Hopefully this is of some interest. I do make mistakes sometimes, be warned...

Here is a plot of the 3c 4b (no ER) scenario:

. Bucklin . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . MDDA. . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . MAMPO . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
DAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . CdlA. . . WV. . . . . . . . . . 
. . . . . . . . . .IBIFA. . . . . . . . DMC AER . . . . . . . . 
. . . . . . . . . . . NWL . . C//A. . . . . . . . . . . . . . . 
. . . . . . . VBV . . . . . . . . . . . Diam(appr). . . . . . . 
. . . . . . . . . EBBV. . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . INE2. . . . . . . . . . . . . . . . . 
. . . . . . . . . . . KOTH. . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . ChainRO . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . IRV . . . . . . . . . . . . . 

view as fixed width here: 
http://lists.electorama.com/pipermail/election-methods-electorama.com//2020-December/

Kevin

 Le mercredi 16 décembre 2020 à 18:13:07 UTC−6, Etjon Basha <etjonbasha at gmail.com> a écrit : 
>Esteemed gentlemen of the EM list, 
>
> Among the risks inherent in following some of the discussion here for some time is that one is apt to 
>start to tinker with rules on their own. Having done so, one is then apt to present his thinking to the 
>EM list to humbly ask whether one has reinvented the wheel or, if not, if the method proposed has any merit. 
>
>The idea is to strike some balance between latter-no-harm and favorite betrayal, perhaps not meeting 
>either but practically meeting both to a good degree, by mimicking how a reasonable voter would vote 
>given some (but not full) knowledge of the situation. 
>
>The method is a variation of Bucklin where the algorithm used to progress into the next round is different. 
>Voters present ranked ballots, truncation and equal ranking allowed. As in Bucklin, majority of first 
>preferences (but only of first preferences) ends the race. If no candidate has such majority, the count 
>proceeds in rounds where each ballot reveals N of their top preferences as follows: 
>
>- at any point, the placeholder winner (candidate(s) with most approvals so far) is revealed 
>
>- whoever has not approved of the placeholder winner yet, reveals one more preference 
>
>- whoever has approved of the placeholder winner and no candidate further below, is stationary 
>
>- whoever has approved of the placeholder winner and some candidates further below, reverts back 
>to revealing only as far down their vote as the placeholder winner 
>
>All “moves” are run concurrently in simulated ignorance of other voters’ moves, all in discrete rounds. 
>When no more moves are possible (all ballots are either exhausted or go as far down in their 
>preferences as the placeholder winner) the placeholder winner is elected. The rules change, mutatis 
>mutandis, where there are two or more placeholder winners at any given round (reveal only your 
>favorite among them, keep going if you approve of neither so far).  
>
>Has something of the sort (or similar enough) been proposed yet to your knowledge? If not, would 
>this indeed meet the design criteria of a compromise between LNH and FB? 
>
>Thank you for your time, 
>
>Etjon Basha 
>
> 
>
>EXAMPLE 1: 
>
>9 voters and 4 candidates, 3 ABC, 2 BDC, 2 CDA 
>
>First round: 3 A, 2 B, 2 C. No candidate has majority, count continues, A in placeholder winner 
>(PW) with 3 approvals.  
>
>Second round: 3 A (approves of PW so no more preferences revealed), 2 BD (reveals one more), 2 CD 
>(reveals one more). D becomes PW with 4 approvals. 
>
>Third round: 3 AB (reveals one more), 2 BD and 2 CD (both approve of PW so no more preferences 
>revealed). B becomes PW with 5 approvals. 
>
>Fourth round: 3 AB, 2 B (approves one more than PW, so goes back to revealing only PW), 2 CDA (reveals 
>one more). A and B become PWs with 5 approvals each. 
>
>Fifth round: 3 A (approves one more than their preferred PW, so goes back to revealing only preferred 
>PW), 2B (no change), 2 CDA (no change). A becomes PW with 5 approvals. 
>
>Sixth round: 3 A, 2 BD (reveals one more), 2 CDA. A still PW with 5 approvals. 
>
>Seventh round: 3 A, 2 BDC, 2 CDA. No more moves possible, current placeholder winner A is elected 
>with 5 approvals. 
>
>In this (admittedly convoluted) example A wins but standard Bucklin would have elected B in round to 
>with 5 approvals, due to A’s votes helping B at A’s expense. 
>
> 
>
>EXAMPLE 2: 
>
>Taken from Warren D. Smith’s February 2014 example of Condorcet contradiction 
>(https://rangevoting.org/CondCoursera.html) 
>
>100 voters, 3 candidates: 35 ABC, 21 BAC, 21 BCA, 21 CAB, 1 ACB, 1 CBA. 
>
>Not going through the process, the method elects B in 3 rounds, while the Condorcet winner is A 
>(incidentally showing this method does not meet Condorcet). In this case, standard Bucklin would have also elected B. 