[EM] Strategy-free criterion

[Chris Benham]

Kevin,

Sorry for the long pause.  Just sticking for a moment with plain ranking 
methods (with no explicit approval cutoff but truncation definitely 
allowed) then I think "Double Defeat (implicit)" is a very useful 
criterion that implies all of Plurality, Minimal Defense and the Strong 
Defensive Strategy Criterion.

If more voters sincerely prefer A to B than vice versa, then the voters 
who prefer A to B can ensure that B doesn't win simply by truncating B 
and not A.  Notice that that set of voters doesn't have to be more than 
half the voters and A doesn't doesn't have to be a sincere CW.

Now to talk about a problem of all preferential methods.  Say there are 
three factions of voters, each with its own candidate. Each faction 
strongly wants its own candidate to win and has no real preference among 
the other two, i.e. is about equally hostile to or disinterested in both 
of them.  Say it is known from polling that candidate A has about 50% 
support and candidates B and C each have about 25%.

A is obviously the highest SU candidate, and with normal natural sincere 
say Approval voting all the voters will truncate two of the candidates 
and A easily wins.  But with a preferential system (especially one that 
meets Clone-Winner, as they all should) the B and C factions
have a huge incentive to do a preference-swap deal. That way each of 
them raise their chance of winning from zero to about 25%.

In light of that, to some even a result like

49 A
26 B>C
25 C>B

can look suspicious. Yes B and C are a perfect set of voted clones and a 
Mutual Majority and B is a voted Condorcet winner, but in the real world 
some might say that the B and C factions "ganged up" on A and 
"manipulated the election".
If voting is optional, the A faction might like to sponsor a minor 
candidate X whose supporters prefer A to B and C but not enough to 
bother voting if X is not on the ballot.  So say that results in just 3 
more ballots, all X>A, then A wins.

Now say we have this much discussed example:

49 A
24 B
27 C>B

By Double Defeat (implicit)  B must win.  But those people who were 
unhappy and cynical and suspicious about A's loss in the first example 
won't accept it in this one.

There are several reasons why voters take lower preferences less 
seriously than election method pundits (especially the Condorcet 
enthusiasts).  Obviously in most places they are used to casting FPP 
ballots.

In Australia voting is compulsory and in most elections truncation is 
not allowed. This would be a big burden on voters who take it seriously 
if it wasn't for the regular custom of parties and sometimes independent 
candidates advising their supporters on how to complete their ballots. 
So a lot of voters are only thinking about which party should get their 
"primary vote", and the lower preferences are just some relatively 
arbitrary formality to ensure that their vote is counted.

And parties who are confident that their voters' lower preferences won't 
be distributed normally just advise their voters to fill out the ballot 
in the way that is most convenient.

I think Double Defeat (implicit) is incompatible with Symmetric 
Completion, a criterion I like.   In the second example I am fine with 
Hare or Benham electing A.

But if the voters can give an explicit approval cutoff and the method 
complies with Double Defeat (explicit) then most potential complaints 
from losers will be much weaker (and of course none will be stronger, 
and the voters get a more expressive ballot).

Chris B.



*Chris Benham*cbenhamau at yahoo.com.au 
<mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Strategy-free%20criterion&In-Reply-To=%3C823bb761-54e0-4228-8cb6-4195a1755c6d%40yahoo.com.au%3E>
/Sun Jun 23 16:31:34 PDT 2024/
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Kevin,

>/If one thinks GMC was contrived just to support Schulze(WV), it's worth 
asking how />/Woodall also managed to invent it (as CDTT). /Too easy. Woodall's  CDTT was merely a set and not a normative
criterion.  He never said that he thought that the winner should come
from the CDTT set.

>/If I could prove that method XYZ was the best at />/sincere Condorcet efficiency (or substitute SU if you prefer), you 
would categorize />/that as mainly a marketing benefit? /
Talking about sincere Condorcet efficiency (and not SU)  among methods
that meet voted Smith, yes.  The sincere (voted or not) CW's status
could be based on some very weak, barely existing, pairwise preferences.
If the identity of this CW has been "concealed" by voters choosing (or
not bothering) to express them, then big deal.

>/I have nothing against explicit cutoffs. /
I'm glad to hear it.  Methods in that category that meet Double Defeat
cut through a few Gordian knots, and render all (or nearly all) of the
rankings-only "defensive strategy" criteria irrelevant.

More on this later.

Chris B.

On 24/06/2024 7:38 am, Kevin Venzke wrote:
>/Hi Chris, />//>/Chris Benham <cbenhamau at yahoo.com.au 
<http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com>> 
a écrit : />>>/What I call inherently of value would be things like sincere Condorcet 
efficiency or />>>/reduced strategic incentives. />>//>>/I can understand voted Smith-set fundamentalism, and that is expensive 
enough. But if />>/there is a top cycle I don't share the mind-set "Probably there is a 
sincere CW />>/(concealed by strategic truncation or order-reversal) and our top 
priority should be to />>/infer or guess who that is and elect him/her."  There may well be no 
sincere CW or a />>/higher SU candidate. So quite nice, but mainly just a marketing benefit. />/I'm not sure how to read this. If I could prove that method XYZ was the 
best at />/sincere Condorcet efficiency (or substitute SU if you prefer), you 
would categorize />/that as mainly a marketing benefit? To me this is the entire thing that 
the method />/is supposed to be doing. />//>>/https://electowiki.org/wiki/Strategy-free_criterion />>//>>/If a Condorcet candidate exists, and if a majority prefers this 
candidate to another />>/candidate, then the other candidate should not win if that majority 
votes sincerely and />>/no other voter falsifies any preferences. />>//>>/I think that is very similar to the Generalised Majority Criterion, />/It's much more limited. />//>>/enough for me to />>/reject it on the same grounds. And even if I didn't have that 
criticism, I don't see />>/why it's something we should care much about. It looks like something 
contrived just to />>/serve as ammunition against Hare and Margins. />/It does have that role, but Hare/Margins already fail the other 
criteria. I have />/always viewed SFC as an explanation of what could be improved in Approval. />//>/I would not say someone needs to care about SFC specifically, but it 
addresses />/truncation incentive, so it isn't useless to satisfy it. />//>>/(And possibly the similar GMC was contrived just to help promote the 
Schulze method.) />/If one thinks GMC was contrived just to support Schulze(WV), it's worth 
asking how />/Woodall also managed to invent it (as CDTT). />//>>/I would think that if the method />>/is making some attempt to minimise the number of "wasted votes", then />>/many voters would want to be able to express their full sincere ranking />>/and also would at least not mind giving their sincere or semi-sincere />>/approval cutoff. />/I have nothing against explicit cutoffs. />//>/Kevin />/votingmethods.net/
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