Strategy-free criterion
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 Benhamcbenhamau 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/
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.
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/
On 2024-08-02 19:35, Chris Benham wrote:
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".
Just to be sure I got what you were saying, this is in an imperfect
information setting, right? The B and C factions don't know which of
them have more first preferences than the other.
I'm assuming that's the case because if they knew, then while the B
faction would be interested in doing a swap to flip the winner from A to
B, the C faction is indifferent to who wins out of A and B, and thus
wouldn't bother.
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.
IMHO, that seems like a significant flaw, because it potentially turns
party-neutral methods (IRV and STV) into something considerably closer
to party list.
Given that it does, it would make sense for the voters to treat higher
ranks as more important than lower ones - because if filling out lower
ranks is a chore, then voters would focus on higher ranks.
Say a voter "independently ranks" those candidates where he neither
copies some other advice or ranks randomly, and "fills" the other
candidates (for lack of better terms).
Then it's possible that the connotation of lower ranks as something that
you fill, not independently rank, carries through to the point that
voters independently rank fewer candidates than they would explicitly
rank if they could truncate.
IRV and STV's focus on higher preferences might also contribute to the
voters' focus, but it's hard to say what the direction of causality is
there: whether these methods were adopted because the public was used to
Plurality-style reasoning, or if their (particularly AV's) compromise
incentive leads the voters to focus further on first preferences.
-km
Kristofer,
Just to be sure I got what you were saying, this is in an imperfect
information setting, right? The B and C factions don't know which of
them have more first preferences than the other.
Yes.
IMHO, that seems like a significant flaw, because it potentially turns
party-neutral methods (IRV and STV) into something considerably closer
to party list.
Not allowing truncation is always silly and unjustified. GIGO.
I gather that historically preferential voting was introduced in
Australia so that the relatively disciplined and organised Labor Party
could be more easily defeated. If truncation was allowed then some lazy
anti-Labor voters might do that. It continues to be justified (among
the few who even think about it) as being in the spirit of compulsory
voting (which I agree does more good than harm.)
The scenario I described with 3 factions and no voters having a sincere
second preference would be very rare and the apparent "flaw" of
preferential methods that meet Clone Winner and Dominant Coalition in
that situation is not one that I'm in favour of trying to address.
STV elections for seats in the Australian Senate are deliberately
"corrupted" to resemble Party List PR. The voter has the option of
voting for a party "above the line" which means that the voter blindly
votes that party's full "ticket" (determined before the election and
accessible to anyone interested). Now if one votes "below the line" by
numbering boxes next to the names of individual candidates you are
allowed to partially truncate (but you still have to rank quite a few,
maybe 12 candidates).
All this unnecessarily gives the party machines unjustified extra
power. They horse-trade among themselves as to where they'll direct
preferences that voters don't care and probably don't even know about.
Chris B.
On 5/08/2024 12:01 am, Kristofer Munsterhjelm wrote:
On 2024-08-02 19:35, Chris Benham wrote:
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".
Just to be sure I got what you were saying, this is in an imperfect
information setting, right? The B and C factions don't know which of
them have more first preferences than the other.
I'm assuming that's the case because if they knew, then while the B
faction would be interested in doing a swap to flip the winner from A
to B, the C faction is indifferent to who wins out of A and B, and
thus wouldn't bother.
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.
IMHO, that seems like a significant flaw, because it potentially turns
party-neutral methods (IRV and STV) into something considerably closer
to party list.
Given that it does, it would make sense for the voters to treat higher
ranks as more important than lower ones - because if filling out lower
ranks is a chore, then voters would focus on higher ranks.
Say a voter "independently ranks" those candidates where he neither
copies some other advice or ranks randomly, and "fills" the other
candidates (for lack of better terms).
Then it's possible that the connotation of lower ranks as something
that you fill, not independently rank, carries through to the point
that voters independently rank fewer candidates than they would
explicitly rank if they could truncate.
IRV and STV's focus on higher preferences might also contribute to the
voters' focus, but it's hard to say what the direction of causality is
there: whether these methods were adopted because the public was used
to Plurality-style reasoning, or if their (particularly AV's)
compromise incentive leads the voters to focus further on first
preferences.
-km