Forest,

I am not enthusiastic about this idea.

In this example all the voters gave their full strict rankings. It isn't
like a cycle was caused by a lot of truncation (or equal-ranking
possible Compromising) and we can say "Some of you may not have felt
sufficiently informed about all the candidates or you forgot
this isn't FPP, so we are gong to have a runoff."

Instead we are saying "We think it highly likely that some of you are
lying so we are going to make you vote again."

Too cynical and insulting.

One of the relatively simple methods I like has been named after me.  It
says  "This is confusing. Can the the favourite of the fewest
please go away."

To get on the ballot at all in public political elections candidates
normally have to show that they have some minimum exclusive
first preference support, but the Condorcet criterion is happy to elect
a candidate with none.

Here is my new suggested Condorcet method:

*Voters rank from the top however may candidates they wish, equal
ranking and truncation allowed. Also they may indicate an
approval cutoff, so they can rank among unapproved candidates. Default
is approving all candidates ranked above at least one candidate.

If there is no CW, ignore rankings among unapproved candidates. If there
is still no CW, then (based on the full rankings) elect the
Smith//Approval winner.*

Chris Benham

On 14/06/2023 11:59 am, Forest Simmons wrote:

Chris,

I like your new Condorcet method, and consider it to be a much more
practical suggestion than any of my sincere CW finder ideas currently in
progress.

The ballot profile you provided to illustrate your LV Sorted Margins burial
resistant method, ended up electing A, which we considered to be better
than electing B, because we thought that with some positive probability the
ballot profile might be a result of the B faction's insincere order
reversal .... changing sincere 44 B>A to 44 B>C, i.e. the B faction burying
A under C ... so that electing B, like just about every other method under
the sun, would encourage bad behavior.

Is it insulting to voters to build in safe guards that make insincere
truncations or burials less likely to pay?

Is it insulting to lock your front door when leaving town for a few dsys?

Borda famously said, "My method is intended for honest voters." [He was
aware of the burial incentive, but like Saari, Maskin, and many others,
apparently unconcerned about the Clone Dependence problem.]

You and I prefer methods that encourage honest voters to stay honest... and
a bicycle lock makes stealing your bike less attractive, but cannot
guarantee protection against the determined thief.

What your example profile shows is that no Universal Domain method can
determine whether or not a ballot set of complete rankings is the result of
burial of a sincere CW.

In fact, to convert B to ballot CW only takes five "unburials" : 5 C>A -->
5 C>B.  while to change C to the ballot CW takes 46 unburials: 46 A>B -->
A>C, and it takes 44 unburials to convert A into the ballot CW: 44 B>C -->
44 B>A.

It looks like B is at least as likely as A to be the sincere CW, if there
is one.  But it is impossible to know for sure without some information
outside of the Universal Domain. ... perhaps some kind of sincere runoff,
or asking Alexa, for example.

Going outside the strict Universal Domain by allowing truncations, equal
rankings, approval cutoffs, or other levers, offer additional
expressiveness that can reduce incentives for burial, compromise, etc.

I've been experimenting with how far we can get with two sets of ballots
... one possibly strategic set, for the purpose of determing the finalists
and runoff order ... and the other set dedicated solely to the kind of
runoff that elects the sincere CW whenever there is one.

And geometric considerations show that when the ballot Smith set has fewer
than four candidates, the existence of a sincere CW is much more likely
than not.

That's why my currently focus is on a three candidate (i.e. worst case
public Smith set) runoff method for which the sincere CW (when there is
one) is the game theoretic winner (assuming perfect information and
rational voting).

Next time, a method that will seem more familiar!

fws

On Wed, Jun 14, 2023, 5:19 PM C.Benham cbenham@adam.com.au wrote:

On 6/15/23 07:47, Forest Simmons wrote:

James Green-Armytage has another suggestion for deterring burial:
https://www.jamesgreenarmytage.com/dodgson.pdf

I haven't read it in detail, so perhaps the devil's in the details about
"plausible assumptions about how candidate decide". But what do you
think of that method?

This is still an interesting venue, of course. I've updated the
Electowiki page about Condorcet loser to include information that a
manual runoff method always passes honest Condorcet loser (assuming no
drop in turnout).

At some point I would like to do a minimum strategy evaluation of
methods with two rounds, but I've currently been occupied with cleaning
up some other code in my election simulator quadelect so that I can
automatically check for clone failures, monotonicity, etc. the same way
I can check for strategy failures; and so that I can classify strategy
failures as burial, compromise, or other.

Maybe, eventually!

-km

On 15/06/2023 7:17 pm, Kristofer Munsterhjelm wrote:

In an earlier article James-Green Armytage discussed different
Condorcet-IRV  methods, naming them all after people. I think there was
Tideman, Woodall and "Benham".

Tideman (and "Smith-AV") fails Mono-add-plump and Mono-append. And both
Tideman and Woodall are more complicated than Benham.

https://www.votingmatters.org.uk/ISSUE29/I29P1.pdf

The "one round version" of what he is now calling "Limited-Round
Dodgson-Hare" is the same as Benham except that it specifies a
"voluntary candidate withdrawal" option
and says nothing about whether equal-ranking should be allowed or how it
should be handled.

I don't like candidate withdrawal options because I think the result
should be determined as much as possible by voters via their ballots
versus the machinations of candidates.

And for a practical proposal I don't like allowing above-bottom
equal-ranking because it makes the method more complicated and/or more
vulnerable to Pushover strategy.

But if it insisted on, then equal rankings (say A=B) should be
provisionally interpreted as giving an equal fraction of a vote summing
to 1, in this case half a vote each to A and B.

Then for the purpose of deciding which if any gets eliminated the A=B
ballots should all be interpreted as giving a whole vote to whichever of
the two had the higher tally on the
fractional basis and nothing to the one that had the lower tally.

From the article you linked you linked to:

I'm a bit sceptical about that. I would have thought that it would make
Hare (aka the Alternative Vote aka IRV) less vulnerable to Compromise
but a bit more vulnerable to Burial.

In terms of criterion compliances the price we pay for gaining Condorcet
is that we lose Later-no-Help, Later-no-Harm and Mono-add-Top.

Chris Benham

On 15/06/2023 7:17 pm, Kristofer Munsterhjelm wrote:

It looks like James Green Armytage's adaptation of Dodgson and Hare boils
down to going as far as possible with repeatedly eliminating non- Smith
candidates during rounds of negotiations and voluntary candidate
withdrawals. Then that process stalls, knock it off dead center by
eliminating the candidate with the fewest first place votes, before
resuming the negotiations, reballotings, candidate withdrawals, etc,
punctuated with additional IRV style Elimination steps when necessary.  If
that process goes on beyond some established number of steps, then you
finish off with IRV or Benham applied to the remaining candidates.

It sounds messy and complicated, but with any luck the original Smith set
will be small, and the negotiations and withdrawals with satisfactorily
resolve things with only one or two sets of ballots.

Armitage is making a heroic effort to resolve the top cycle without going
outside the Universal Domain except for informal, low pressure negotiation
sessions encouraging candidates to withdraw and voters to reconsider their
votes.

He never mentions Dodgson's simpler and more elegant method that we call
Asset Voting or Candidate Proxy ... because that would be a much more
radical departure from Universal Domain.

For the same reason he makes no mention of his previous progress with
Pairwise principles applied to Score/ Range style ballots.

I think that just plain Benham with a one time candidate withdrawal option
would get most of the benefit of the proposal without the perceived
complexity.

Here's an idea that came to me while reading the paper:

At every stage eliminate the pairwise loser PL of the two remaining
candidates with the smallest minimum pairwise support ... along with every
candidate defeated by PL.

When there is only one candidate left, elect the sincere winner between it
and the last PL candidate.

Indignant voters can say, "Thank you very much, but I always vote
sincerely," while admitted sinners can include a second set of ballots for
use in the sincere binary runoff.

I suggest using min PS instead of first place votes because transferred
first place votes require additional passes through the ballots, while min
Pairwise Support counts do not, since all of the necessary information is
in the initial pairwise support matrix ... and the fewer the uneliminated
candidates, the more accurately the minPS values reflect the first place
transferred vote counts.

fws

On Thu, Jun 15, 2023, 2:48 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

Chris,

What do you think of Benham based on minPS (relative to remaining
candidates) instead of min  transfered votes?

On Thu, Jun 15, 2023, 1:17 PM C.Benham cbenham@adam.com.au wrote:

First a definition:

A candidate X is an enemy of a pair if it beats both of its members.

New Method:

Elect the CW if there is one.

Else elect the sincere winner of the strongest pair that has no enemies, if
there is such a pair.

Else elect the sincere winner of the pair whose enemy first place count  is
smallest.

fws

On Thu, Jun 15, 2023, 1:17 PM C.Benham cbenham@adam.com.au wrote:

On 6/15/23 22:17, C.Benham wrote:

I can see that reasoning; it's similar to why I don't like candidate
ordering methods (where the published ordering given by the voter's
favorite completes the ballot).

In a situation where there's an honest CW, it should be fairly well
known who that CW is... I would imagine. But it's hard to tell how it
would turn out in practice.

If I got it right, the claim in Durand's paper is:

Suppose that the winner of an election E according to method M is M(E).
(An election consists of one or more fully ranked ballots - no
truncation or equal-rank.)

Suppose that M has the property that a cooperating majority that knows
how everybody else is going to vote can force any outcome it wants.
(This is called InfMC and is a weaker majority criterion; Borda passes
it though it fails ordinary majority.)

Suppose that M* is the method: "Elect the Condorcet winner if one
exists, otherwise elect the winner of M".

Define that, if, for an election E, it's possible for a group of voters
who all prefer some candidate A to the winner W elected by M, to make A
win instead of W by altering their ballots, then E is coalitionally
manipulable under M.

Then: if M passes InfMC, and if an election E is coalitionally
manipulable under M*, then it must also be coalitionally manipulable
under M.

The nature of the manipulation may differ: e.g. it could be burial under
M* and compromising under M, for instance if strategy is towards the CW
under M and away from the CW under M*.

(In short, if in a given election, it's possible for a group to modify
their ballots to change the winner to someone they all prefer to the
winner, in method Condorcet//M, then it's also possible in method M, if
M passes InfMC. The strategy, group, and winners may differ.)

If truncation or equal rank is allowed, then the property holds as long
as "Condorcet winner" is defined in an absolute sense: that for any B
there exists a group of more than 50% of the voters who prefer A to B;
but electing "relative" Condorcet winners (ones where more people prefer
A to B than B to A) can make previously unmanipulable elections manipulable.

(Kevin, Forest: If I got that wrong, feel free to correct it :-)

-km

A a couple of clarifications below that time did not allow on the first go
around
...

On Fri, Jun 16, 2023, 11:43 AM Forest Simmons forest.simmons21@gmail.com
wrote:

Sincere winner found by ballots designated "sincere" in the case of voters
that do not need to include a second ranked preference ballot for the
sincere  two candidate runoff.

of the strongest pair that has no enemies, if there is such a pair.

In practice such a pair always exists, so the rest of the definition below
is just a tecnicality to cover a statistical impossibility on a par with
winning the lottery jackpot and getting hit by lightening on the same day.

...

[Meaning the total of all the first place counts of all of the enemies of
the pair, if it has any]

is smallest.

Note that the sincere runoff is a kind of max potential information runoff,
because the strongest defeat is the last one you would expect to be
reversed under sincere votes.

If it is reversed, you very likely just thwarted a strategic voting
attack.

If not, you just got excellent confirmation that the right candidate was
elected.

In other words, the method, besides being very decisive, is not likely to
reward manipulators ... two features that tend to build much needed voter
confidence in the validity of election results.

fws