The superiority of sport to politics is that sports have independent
referees. Referees have rules of independence unlike many referendums.
In the US city referendums, the Machine, such as Tammany Hall in New
York and about 20 American cities used referendums as battering rams to
reinstate monopolistic elections against proportional representation
with a single transferable vote. Likewise Britain has no referendum
rules and is fine with money and publicity deciding the issue.

Paddy Ashdown, former Liberal Democrat leader, said of the 2011
Alternative Vote referendum: "They marshalled a regiment of lies." And
IRV is still monopolistic, despite the ranked choice vote. It's a basc
principle of scientific investigation not to prejudge what one is
supposed to prove. A representative sample of self-informing public
opinion, a Citizens Assembly, can be a referee. As it was in British
Columbia, with independence rules, before the politicians lost
self-restraint and rigged the referendum rules, with a one and a half
votes weighting in favor of FPTP (double 60% thresholds).

The relevance of all this, in case you're wondering, is that there is no
authoritative "standard model" of elections, as there is a standard
model in physics, despite its acknowledged imperfections. Therefore, it
follows that election implementation is not the decision of experts, as
it would be, regarding phyics or biology, for instance, but has to have
the crude fall-back of referee devices like a Citizens Assembly, which
reformers in Canada widely seem to recognise.

Regards,

Richard Lung.

On 22/03/2023 04:00, Forest Simmons wrote:

Time for an example or two.

48 C
28 A>B
24 B

A>B 28 to 24
B>C 52 to 48
C>A 48 to 28

The respective minPS scores are their Top counts 28, 24, &48
So C is the offensive champ with MaxminPS(C)=48.

MaxPO(C)=52 (from B)

A and B are tied for minMaxPO at 48 from C. This tie is broken by looking
at the other PO scores 24 and 28, respectively. So A is the minMaxPO
candidate (defensive champ) with MaxPO(A)=48+24epsilon, ehich is less than
MaxPO(B)=48+28epsilon, and (as already noted) less than MaxPO(C)=52.

Since the Offensive Champ C beats the Defensive Champ A, (48 to 28) and
there is no undefeated candidate, our tournament method elects C.

Now let's look at ...

a A>B(sincere A>C)
b B>C
c C>A

If the A faction is largest its burial of the sincere CW C pays., but the
because A is both the Offensive Champ and the Defensive Champ with
minPS(A)=a.

But suppose C takes the customary sincere CW precaution of bullet voting:

a A>B
b B>C
c C

Then the respective minPS scores are a, b, and c.

Continuing our assumption that enabled the A faction to bury C with
impunity ... namely a>max(b,c), we see that A retains its status as
Offensive Champ with minPS(A)=a>max(b,c).

The MaxPO's are now ...
(b+c)=MaxPO(A), a=MaxPO(B), and (a+b)=MaxPO(C).

The min of these is a=MaxPO(B). So B is the Defensive Champ.

The pairwise contest between the two champs is A vs B ... which still lets
the A faction get away with its burial of the sincere CW.

We see that under this method the sincere CW is at the mercy of the largest
faction.

So despite the nice sports tournament heuristic... we cannot endorse this
method!

It's a good thing we have better methods that are conceptually and
operationally just as simple ... if not as innately appealing to sports
enthusiasts.

Is there a better pair of fall back candidates to choose between when there
is no ballot CW?

How about the implicit approval candidate versus the Max Equal Top
candidate?

The beauty of this class of methods is only one pass through the ballots,
as long as the two contenders are kept simple enough.

-Forest

On Tue, Mar 21, 2023, 9:00 PM Forest Simmons forest.simmons21@gmail.com
wrote:

On 3/22/23 05:00, Forest Simmons wrote:

I'll have to investigate further, but my impression from working with
burial-resistant methods is that it's impossible to make a method that's
burial resistant (in the DMTCBR sense) without using positional data.

However, another important property to note is that the modes of
strategy very much depend on how the data is gathered. In an election
situation, burial is fairly easy: just change A>X>B>C>D>E>F into
A>B>C>D>E>F>X. But in sports, the analog would be that A decides to tell
B to "strategically defeat X", e.g. to score more goals against X (or
similar) to push X further down the ranking. Presumably any team B would
be doing its best to defeat X already, so "burial" doesn't really seem
to be a strategy in sports.

Thus it's not a problem that we don't have positional data, because we
don't need to defend against that particular strategy.

In sports, what strategies could exist? I'd imagine something more
like... team B tells team X to play badly against team C, because the
tiebreaker won't make X win anyway. Thus if say, the Smith set is ABCX,
then it's possible that X losing more heavily against C could make B win
instead of A. That's more like compromising, but it's not quite the same
thing.

-km

"In sports, what strategies could exist? I'd imagine something more like... team B tells team X to play badly against team C, because the tiebreaker won't make X win anyway. Thus if say, the Smith set is ABCX, then it's possible that X losing more heavily against C could make B win instead of A. That's more like compromising, but it's not quite the same thing."

AFAIK the majority of deliberate losing (or not winning as handily as one is capable) in sports are to take advantage of side bets.  I can imagine that in a double elimination tournament one might deliberately go over to the loser's bracket to avoid a team one is particularly bad against, in the hope that they'll be eliminated before you have to face them.  But that means you have to fight your way through the loser's bracket, which means more matches; I don't know that it would be worth it most of the time.

The other scenario I am aware of is that in chess and some other sports, one can lose or not win as big to avoid having your rating increased, so that (again) you get to face lesser opposition.  This definitely happens.

I'm not sure how much of this carries over to an election situation, though.

--pH

-----Original Message-----
From: Election-Methods election-methods-bounces@lists.electorama.com On Behalf Of Kristofer Munsterhjelm
Sent: Wednesday, March 22, 2023 8:03 AM
To: Forest Simmons forest.simmons21@gmail.com; EM Election-methods@lists.electorama.com; Kevin Venzke stepjak@yahoo.fr; Andy Jennings elections@jenningsstory.com; Colin Champion colin.champion@routemaster.app; Andy Dienes andydienes@gmail.com
Subject: Re: [EM] Simple Tournament Proposal

On 3/22/23 05:00, Forest Simmons wrote:

I'll have to investigate further, but my impression from working with burial-resistant methods is that it's impossible to make a method that's burial resistant (in the DMTCBR sense) without using positional data.

However, another important property to note is that the modes of strategy very much depend on how the data is gathered. In an election situation, burial is fairly easy: just change A>X>B>C>D>E>F into
A>B>C>D>E>F>X. But in sports, the analog would be that A decides to tell
B to "strategically defeat X", e.g. to score more goals against X (or
similar) to push X further down the ranking. Presumably any team B would be doing its best to defeat X already, so "burial" doesn't really seem to be a strategy in sports.

Thus it's not a problem that we don't have positional data, because we don't need to defend against that particular strategy.

In sports, what strategies could exist? I'd imagine something more like... team B tells team X to play badly against team C, because the tiebreaker won't make X win anyway. Thus if say, the Smith set is ABCX, then it's possible that X losing more heavily against C could make B win instead of A. That's more like compromising, but it's not quite the same thing.

-km

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All of this groping for a halfway decent Quick & Clean tournament method
has brought me to this:

Lacking an undefeated candidate, elect the candidate who defeats the
Defensive Champ with the most winning votes.

To define the Defensive Champ, we need to know for each pair of candidates
X and Y the number of ballots on which Y was ranked ahead of X ... this is
the Pairwise Opposition of Y against X, denoted PO(Y,X)

The MaxPO of X or MPO(X) is the greatest value of PO(Y,X) as Y ranges over
all of X's opponents. This MPO(X) is X's defensive score ... the smaller
the better ... it is the most "points" (votes) any opponent of X has made
against X in any pairwise matchup of this election.

The Defensive Champ is argminMPO(X), the candidate whose MPO value is
smaller than any other candidates MPO value.

So the Defensive Champ is the one who "lets slip" the fewest votes to any
of her opponents ... almost as if she had some psychic power to keep votes
against her from reaching the ballot box.

So this Defensive Champ is a strong candidate ... but the candidate that
overcomes that strong resistance and gets the most votes past her defense
is even stronger ... and that's the one our method chooses!

Example:

a A>B (Sincere A>C)
b B>C
c C>A

The MPO's of the respective candidates are MPO(A)=(n-a), MPO(B)=(n-b), and
MPO(C)=(n-c). So the Defensive Champ is A, assuming the A faction is
largest (emboldening the burial).

The winner is supposed to be the candidate with the strongest defeat
against the Defensive Champ A. So C is the only candidate that qualifies,
since no other candidate defeats A.

So we see that the sincere CW is restored.

Example 2.

48 C
28 A>B
24 B(Sincere B>A)

In a previous message we found that the Defensive Champ was A, who is
defeated only by C ... therefore the winner.

So the B faction's defection backfired.

So far, so good ... not at all surprising ... because I had these examples
in mind when I designed this method;-)

We need somebody to run some tests.

-Forest

On Wed, Mar 22, 2023, 7:31 AM Hahn, Paul manynote@wustl.edu wrote:

Is clone dependence a problem ... teaming or crowding in tournaments?

On Wed, Mar 22, 2023, 7:31 AM Hahn, Paul manynote@wustl.edu wrote:

On 22.03.2023 18:54, Forest Simmons wrote:

In one sense, every method might be clone dependent. Suppose that
playing against, say a positional chess player is draining and requires
a lot of concentration. Then if you face a particular positional player
ten times instead of one, it might do such a number on your endurance
that even though you beat them all, you lose other contests you might
have won, thus making you lose in the end.

However, if we suppose that A>B always leads to A>B1, A>B2, A>B3 etc.,
then it depends only on the tournament format and not on your endurance
as a player. Round-robin tournaments where wins count x points, ties 1,
and losses zero would reduce to Copeland and could have crowding
problems. Accelerated systems (e.g. Swiss) would probably also be
vulnerable to the rating strategy that Paul mentioned, although this
definitely isn't my area of expertise.

I guess that elimination tournaments could also be clone vulnerable - it
would depend on the seed order. An interesting question would be: what
property needs to hold for a seed and bye system for the resulting
elimination tournament to be cloneproof? Does any such rule exist?
Dealing with byes in particular seems very tricky.

Seed systems also have other requirements, like strong players not
meeting too early, which could further constrain the field of viable
systems. While searching, I found this paper, but I have only cursorily
looked at it:
http://www.oxfordcroquet.com/tech/knockout3/What_is_the_Correct_Way_to_Seed_a_Knockout_Tournam.pdf

-km