[EM] Schulze Method shortcut

[John]

Forgot to say: please copy me on all responses, as I am not currently
receiving list messages.

Hi all! I'm investigating election methods as part of a general interest
in political things (I've run for Congress, developed economic policies,
and am seriously considering opening an elections consulting firm due to
recent failures in election security). I wanted to ask a few questions
here.
The Schulze method elects from the Schwartz set using a beatpath
algorithm. The usual explanation is incredibly complex, and complexity is
undesirable but often necessary. Would this method be equivalent?
1. Eliminate all candidates not in the Schwartz set.
2. If there is one candidate left, elect that candidate.
3. Exclude the pairwise race with the smallest win margin.
4. Repeat.
Tideman's Alternative Schwartz is this, except #3 eliminates the candidate
with the fewest first-rank votes. I am leaning toward Tideman's
Alternative Schwartz or Smith for their simplicity and resistance to
tactical voting and nomination.
Thanks.
—John

[Markus Schulze]

This post might be inappropriate. Click to display it.

[John]

Hi,
I suspect you didn't receive the below email since Markus Schulze
elected to not copy you onto his response. I've decided to thus foward
it to you.
Kind regards,
Arthur Wist
---------- Forwarded message ----------
Date: 7 August 2018 at 18:41
Subject: Re: [EM] Schulze Method shortcut
Hallo,

The Schulze method elects from the Schwartz set using a beatpath
algorithm. The usual explanation is incredibly complex, and complexity

is

undesirable but often necessary. Would this method be equivalent?
1. Eliminate all candidates not in the Schwartz set.
2. If there is one candidate left, elect that candidate.
3. Exclude the pairwise race with the smallest win margin.
4. Repeat.
Tideman's Alternative Schwartz is this, except #3 eliminates the

candidate

with the fewest first-rank votes. I am leaning toward Tideman's
Alternative Schwartz or Smith for their simplicity and resistance to
tactical voting and nomination.

(1) The best possible election method according to the underlying heuristic
of instant-runoff voting will always be instant-runoff voting. Therefore,
I don't think that any supporter of instant-runoff voting will be convinced
by a hybrid of Condorcet voting and instant-runoff voting.
(2) The Schulze method satisfies monotonicity and reversal symmetry.
Instant-runoff voting and Tideman's alternative methods violate
monotonicity and reversal symmetry. Therefore, monotonicity and
reversal symmetry cannot be used anymore as arguments against
instant-runoff voting.

IRV tends to squeeze out candidates with weak first-rank votes but strong
second-rank votes.

(3) Promoting a hybrid of Condorcet voting and instant-runoff voting
will make the audience believe that there is a fundamental problem
when there is no Condorcet winner and that every possible way to solve
a situation without a Condorcet winner necessarily contains arbitrary
decisions. However, election methods like the Schulze method solve
situations without a Condorcet winner in a consistent manner without
having to step outside their underlying heuristic, without having to
resort to some other method, and without having to sacrifice
compliance with important criteria.

Condorcet methods are Smith-efficient: they identify a
particularly-suitable set of candidates meeting a sort of mutual majority
criteria (strong support overall) and elect from that. When that set is
exactly one candidate, it is the Condorcet candidate.

Because these attempt to identify a strong candidate instead of a "winner"
(someone with a certain number of votes—the most, a majority, or a quota),
they can have some difficulty finding a resolution. That is to say: the
strongest candidate defeats all others; yet that candidate may not exist,
and so you find a set of such strong candidates.

Each underlying heuristic, thus, is designed to identify a particular
strong candidate—a "winner"—in a way which elects from this set of strong
candidates. They're influenced in different ways (best ranking overall
versus most broad acceptance or whatnot; one method even attempts to change
the fewest votes to elect the candidate "closest to being the Condorcet
candidate").

This decision is, itself, an arbitrary one: you select one of these voting
systems based on how you feel about picking one of multiple eligible
suitors. Score voters would probably lean toward Schulze more than Ranked
Pairs because Schulze does something more akin to finding the candidate
with the best marginal utility instead of the strongest rankings.

Any ISDA method effectively throws out non-Smith candidates. Doing so
explicitly is thus similar in theory to using any so-called Condorcet
method. Tideman's Alternative Smith, for example, might find the plurality
first-rank loser (which IRV eliminates) is a strong candidate in the Smith
set, and second rank on many non-Smith-first-rank ballots, thus eliminating
some other Smith candidate first. This can lead to that candidate winning.

Alternative Smith *is* an underlying heuristic; while any ISDA method like
Schulze is effectively "eliminate all non-Schwartz candidates and apply
this heuristic" because the heuristic eliminates all non-Schwartz
candidates. The same is true of Ranked Pairs and other ISDA methods.
Schulze and Ranked Pairs have much-more-complex heuristics than Alternative
Smith.

(4) "I am leaning toward Tideman's Alternative Schwartz or Smith

for their simplicity and resistance to tactical voting and nomination."
I don't see why Tideman's alternative methods are supposed to be more
resistant to tactical voting and nomination.

It inherits that from IRV.

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

Markus Schulze
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kevin Venzke]

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[John]

There is a theory that later-no-harm is not desirable, and satisfying
participation proper may not be desirable either by similar logic.

I'm not certain about Mono-Add-Top. Alternative smith fails monotonicity;
although by adding a ballot that ranks X strictly above all candidates, X
(winner) would necessarily have a larger plurality first-vote than Y. If Y
is in the Smith set already, it has fewer plurality first-votes than X, and
retains this going down the rounds, so ranking X first should keep it ahead
of Y in the elimination order.

You can add a ballot that ranks only X and removes candidate Z from the
Smith set, strengthening Y and causing Y to defeat X. To me, this seems
unlikely; or, rather, it seems unlikely to matter in practice. You'll find
that X has to be strong enough with voters to be in the running anyway, so
your best bet is to vote—and if you keep casting ballots that rank X above
everyone else, X is eventually going to become the majority winner. These
are anomalies along the way.

Post by Kevin Venzke
Note that Condorcet methods aren't necessarily Smith-efficient. (For
example, plain minmax methods, or
"Condorcet//Approval".) At least one Condorcet method satisfies
mono-add-top, but Smith methods, in my
opinion, probably can't.
I don't think it's worth worrying about Participation too much. Satisfying
Participation seems to greatly
constrain what kinds of logic a method can use. And the people who
advocate methods that satisfy Participation
probably aren't so dedicated to that aspect in particular.
Kevin
Hi,
I suspect you didn't receive the below email since Markus Schulze
elected to not copy you onto his response. I've decided to thus foward
it to you.
Kind regards,
Arthur Wist
---------- Forwarded message ----------
Date: 7 August 2018 at 18:41
Subject: Re: [EM] Schulze Method shortcut
Hallo,

The Schulze method elects from the Schwartz set using a beatpath
algorithm. The usual explanation is incredibly complex, and complexity

is

undesirable but often necessary. Would this method be equivalent?
1. Eliminate all candidates not in the Schwartz set.
2. If there is one candidate left, elect that candidate.
3. Exclude the pairwise race with the smallest win margin.
4. Repeat.
Tideman's Alternative Schwartz is this, except #3 eliminates the

candidate

with the fewest first-rank votes. I am leaning toward Tideman's
Alternative Schwartz or Smith for their simplicity and resistance to
tactical voting and nomination.

(1) The best possible election method according to the underlying heuristic
of instant-runoff voting will always be instant-runoff voting. Therefore,
I don't think that any supporter of instant-runoff voting will be convinced
by a hybrid of Condorcet voting and instant-runoff voting.
(2) The Schulze method satisfies monotonicity and reversal symmetry.
Instant-runoff voting and Tideman's alternative methods violate
monotonicity and reversal symmetry. Therefore, monotonicity and
reversal symmetry cannot be used anymore as arguments against
instant-runoff voting.
IRV tends to squeeze out candidates with weak first-rank votes but strong
second-rank votes.
(3) Promoting a hybrid of Condorcet voting and instant-runoff voting
will make the audience believe that there is a fundamental problem
when there is no Condorcet winner and that every possible way to solve
a situation without a Condorcet winner necessarily contains arbitrary
decisions. However, election methods like the Schulze method solve
situations without a Condorcet winner in a consistent manner without
having to step outside their underlying heuristic, without having to
resort to some other method, and without having to sacrifice
compliance with important criteria.
Condorcet methods are Smith-efficient: they identify a
particularly-suitable set of candidates meeting a sort of mutual majority
criteria (strong support overall) and elect from that. When that set is
exactly one candidate, it is the Condorcet candidate.
Because these attempt to identify a strong candidate instead of a "winner"
(someone with a certain number of votes—the most, a majority, or a quota),
they can have some difficulty finding a resolution. That is to say: the
strongest candidate defeats all others; yet that candidate may not exist,
and so you find a set of such strong candidates.
Each underlying heuristic, thus, is designed to identify a particular
strong candidate—a "winner"—in a way which elects from this set of strong
candidates. They're influenced in different ways (best ranking overall
versus most broad acceptance or whatnot; one method even attempts to change
the fewest votes to elect the candidate "closest to being the Condorcet
candidate").
This decision is, itself, an arbitrary one: you select one of these
voting systems based on how you feel about picking one of multiple eligible
suitors. Score voters would probably lean toward Schulze more than Ranked
Pairs because Schulze does something more akin to finding the candidate
with the best marginal utility instead of the strongest rankings.
Any ISDA method effectively throws out non-Smith candidates. Doing so
explicitly is thus similar in theory to using any so-called Condorcet
method. Tideman's Alternative Smith, for example, might find the plurality
first-rank loser (which IRV eliminates) is a strong candidate in the Smith
set, and second rank on many non-Smith-first-rank ballots, thus eliminating
some other Smith candidate first. This can lead to that candidate winning.
Alternative Smith *is* an underlying heuristic; while any ISDA method
like Schulze is effectively "eliminate all non-Schwartz candidates and
apply this heuristic" because the heuristic eliminates all non-Schwartz
candidates. The same is true of Ranked Pairs and other ISDA methods.
Schulze and Ranked Pairs have much-more-complex heuristics than Alternative
Smith.
(4) "I am leaning toward Tideman's Alternative Schwartz or Smith
for their simplicity and resistance to tactical voting and nomination."
I don't see why Tideman's alternative methods are supposed to be more
resistant to tactical voting and nomination.
It inherits that from IRV.
http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf
Markus Schulze
----
Election-Methods mailing list - see http://electorama.com/em for list info
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Pareto Man]

Hi Markus,

I would appreciate any feedback you can give on this game I adapted from
Nicky Case. https://paretoman.github.io/ballot/log.html

What method would you call this? It isn't exactly Schulze beatpath. I
would describe it as pair elimination.

Paretoman

Post by John
There is a theory that later-no-harm is not desirable, and satisfying
participation proper may not be desirable either by similar logic.
I'm not certain about Mono-Add-Top. Alternative smith fails monotonicity;
although by adding a ballot that ranks X strictly above all candidates, X
(winner) would necessarily have a larger plurality first-vote than Y. If Y
is in the Smith set already, it has fewer plurality first-votes than X, and
retains this going down the rounds, so ranking X first should keep it ahead
of Y in the elimination order.
You can add a ballot that ranks only X and removes candidate Z from the
Smith set, strengthening Y and causing Y to defeat X. To me, this seems
unlikely; or, rather, it seems unlikely to matter in practice. You'll find
that X has to be strong enough with voters to be in the running anyway, so
your best bet is to vote—and if you keep casting ballots that rank X above
everyone else, X is eventually going to become the majority winner. These
are anomalies along the way.

Post by Kevin Venzke
Note that Condorcet methods aren't necessarily Smith-efficient. (For
example, plain minmax methods, or
"Condorcet//Approval".) At least one Condorcet method satisfies
mono-add-top, but Smith methods, in my
opinion, probably can't.
I don't think it's worth worrying about Participation too much.
Satisfying Participation seems to greatly
constrain what kinds of logic a method can use. And the people who
advocate methods that satisfy Participation
probably aren't so dedicated to that aspect in particular.
Kevin
Hi,
I suspect you didn't receive the below email since Markus Schulze
elected to not copy you onto his response. I've decided to thus foward
it to you.
Kind regards,
Arthur Wist
---------- Forwarded message ----------
Date: 7 August 2018 at 18:41
Subject: Re: [EM] Schulze Method shortcut
Hallo,

The Schulze method elects from the Schwartz set using a beatpath
algorithm. The usual explanation is incredibly complex, and complexity

is

undesirable but often necessary. Would this method be equivalent?
1. Eliminate all candidates not in the Schwartz set.
2. If there is one candidate left, elect that candidate.
3. Exclude the pairwise race with the smallest win margin.
4. Repeat.
Tideman's Alternative Schwartz is this, except #3 eliminates the

candidate

with the fewest first-rank votes. I am leaning toward Tideman's
Alternative Schwartz or Smith for their simplicity and resistance to
tactical voting and nomination.

(1) The best possible election method according to the underlying heuristic
of instant-runoff voting will always be instant-runoff voting. Therefore,
I don't think that any supporter of instant-runoff voting will be convinced
by a hybrid of Condorcet voting and instant-runoff voting.
(2) The Schulze method satisfies monotonicity and reversal symmetry.
Instant-runoff voting and Tideman's alternative methods violate
monotonicity and reversal symmetry. Therefore, monotonicity and
reversal symmetry cannot be used anymore as arguments against
instant-runoff voting.
IRV tends to squeeze out candidates with weak first-rank votes but strong
second-rank votes.
(3) Promoting a hybrid of Condorcet voting and instant-runoff voting
will make the audience believe that there is a fundamental problem
when there is no Condorcet winner and that every possible way to solve
a situation without a Condorcet winner necessarily contains arbitrary
decisions. However, election methods like the Schulze method solve
situations without a Condorcet winner in a consistent manner without
having to step outside their underlying heuristic, without having to
resort to some other method, and without having to sacrifice
compliance with important criteria.
Condorcet methods are Smith-efficient: they identify a
particularly-suitable set of candidates meeting a sort of mutual majority
criteria (strong support overall) and elect from that. When that set is
exactly one candidate, it is the Condorcet candidate.
Because these attempt to identify a strong candidate instead of a
"winner" (someone with a certain number of votes—the most, a majority, or a
quota), they can have some difficulty finding a resolution. That is to
say: the strongest candidate defeats all others; yet that candidate may
not exist, and so you find a set of such strong candidates.
Each underlying heuristic, thus, is designed to identify a particular
strong candidate—a "winner"—in a way which elects from this set of strong
candidates. They're influenced in different ways (best ranking overall
versus most broad acceptance or whatnot; one method even attempts to change
the fewest votes to elect the candidate "closest to being the Condorcet
candidate").
This decision is, itself, an arbitrary one: you select one of these
voting systems based on how you feel about picking one of multiple eligible
suitors. Score voters would probably lean toward Schulze more than Ranked
Pairs because Schulze does something more akin to finding the candidate
with the best marginal utility instead of the strongest rankings.
Any ISDA method effectively throws out non-Smith candidates. Doing so
explicitly is thus similar in theory to using any so-called Condorcet
method. Tideman's Alternative Smith, for example, might find the plurality
first-rank loser (which IRV eliminates) is a strong candidate in the Smith
set, and second rank on many non-Smith-first-rank ballots, thus eliminating
some other Smith candidate first. This can lead to that candidate winning.
Alternative Smith *is* an underlying heuristic; while any ISDA method
like Schulze is effectively "eliminate all non-Schwartz candidates and
apply this heuristic" because the heuristic eliminates all non-Schwartz
candidates. The same is true of Ranked Pairs and other ISDA methods.
Schulze and Ranked Pairs have much-more-complex heuristics than Alternative
Smith.
(4) "I am leaning toward Tideman's Alternative Schwartz or Smith
for their simplicity and resistance to tactical voting and nomination."
I don't see why Tideman's alternative methods are supposed to be more
resistant to tactical voting and nomination.
It inherits that from IRV.
http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf
Markus Schulze
----
Election-Methods mailing list - see http://electorama.com/em for list info
----
Election-Methods mailing list - see http://electorama.com/em for list info

----
Election-Methods mailing list - see http://electorama.com/em for list info

[Pareto Man]

Hi Markus,

I realize now that the method I was wondering about is just common old
minimax. I am thinking it would be cool to add a Schulze beatpath. I
guess I would do it by finding the Schwartz set like John moser suggested.

Paul

Post by Pareto Man
Hi Markus,
I would appreciate any feedback you can give on this game I adapted from
Nicky Case. https://paretoman.github.io/ballot/log.html
What method would you call this? It isn't exactly Schulze beatpath. I
would describe it as pair elimination.
Paretoman

Post by John
There is a theory that later-no-harm is not desirable, and satisfying
participation proper may not be desirable either by similar logic.
I'm not certain about Mono-Add-Top. Alternative smith fails
monotonicity; although by adding a ballot that ranks X strictly above all
candidates, X (winner) would necessarily have a larger plurality first-vote
than Y. If Y is in the Smith set already, it has fewer plurality
first-votes than X, and retains this going down the rounds, so ranking X
first should keep it ahead of Y in the elimination order.
You can add a ballot that ranks only X and removes candidate Z from the
Smith set, strengthening Y and causing Y to defeat X. To me, this seems
unlikely; or, rather, it seems unlikely to matter in practice. You'll find
that X has to be strong enough with voters to be in the running anyway, so
your best bet is to vote—and if you keep casting ballots that rank X above
everyone else, X is eventually going to become the majority winner. These
are anomalies along the way.

Post by Kevin Venzke
Note that Condorcet methods aren't necessarily Smith-efficient. (For
example, plain minmax methods, or
"Condorcet//Approval".) At least one Condorcet method satisfies
mono-add-top, but Smith methods, in my
opinion, probably can't.
I don't think it's worth worrying about Participation too much.
Satisfying Participation seems to greatly
constrain what kinds of logic a method can use. And the people who
advocate methods that satisfy Participation
probably aren't so dedicated to that aspect in particular.
Kevin
Hi,
I suspect you didn't receive the below email since Markus Schulze
elected to not copy you onto his response. I've decided to thus foward
it to you.
Kind regards,
Arthur Wist
---------- Forwarded message ----------
Date: 7 August 2018 at 18:41
Subject: Re: [EM] Schulze Method shortcut
Hallo,

The Schulze method elects from the Schwartz set using a beatpath
algorithm. The usual explanation is incredibly complex, and

complexity is

undesirable but often necessary. Would this method be equivalent?
1. Eliminate all candidates not in the Schwartz set.
2. If there is one candidate left, elect that candidate.
3. Exclude the pairwise race with the smallest win margin.
4. Repeat.
Tideman's Alternative Schwartz is this, except #3 eliminates the

candidate

with the fewest first-rank votes. I am leaning toward Tideman's
Alternative Schwartz or Smith for their simplicity and resistance to
tactical voting and nomination.

(1) The best possible election method according to the underlying heuristic
of instant-runoff voting will always be instant-runoff voting. Therefore,
I don't think that any supporter of instant-runoff voting will be convinced
by a hybrid of Condorcet voting and instant-runoff voting.
(2) The Schulze method satisfies monotonicity and reversal symmetry.
Instant-runoff voting and Tideman's alternative methods violate
monotonicity and reversal symmetry. Therefore, monotonicity and
reversal symmetry cannot be used anymore as arguments against
instant-runoff voting.
IRV tends to squeeze out candidates with weak first-rank votes but
strong second-rank votes.
(3) Promoting a hybrid of Condorcet voting and instant-runoff voting
will make the audience believe that there is a fundamental problem
when there is no Condorcet winner and that every possible way to solve
a situation without a Condorcet winner necessarily contains arbitrary
decisions. However, election methods like the Schulze method solve
situations without a Condorcet winner in a consistent manner without
having to step outside their underlying heuristic, without having to
resort to some other method, and without having to sacrifice
compliance with important criteria.
Condorcet methods are Smith-efficient: they identify a
particularly-suitable set of candidates meeting a sort of mutual majority
criteria (strong support overall) and elect from that. When that set is
exactly one candidate, it is the Condorcet candidate.
Because these attempt to identify a strong candidate instead of a
"winner" (someone with a certain number of votes—the most, a majority, or a
quota), they can have some difficulty finding a resolution. That is to
say: the strongest candidate defeats all others; yet that candidate may
not exist, and so you find a set of such strong candidates.
Each underlying heuristic, thus, is designed to identify a particular
strong candidate—a "winner"—in a way which elects from this set of strong
candidates. They're influenced in different ways (best ranking overall
versus most broad acceptance or whatnot; one method even attempts to change
the fewest votes to elect the candidate "closest to being the Condorcet
candidate").
This decision is, itself, an arbitrary one: you select one of these
voting systems based on how you feel about picking one of multiple eligible
suitors. Score voters would probably lean toward Schulze more than Ranked
Pairs because Schulze does something more akin to finding the candidate
with the best marginal utility instead of the strongest rankings.
Any ISDA method effectively throws out non-Smith candidates. Doing so
explicitly is thus similar in theory to using any so-called Condorcet
method. Tideman's Alternative Smith, for example, might find the plurality
first-rank loser (which IRV eliminates) is a strong candidate in the Smith
set, and second rank on many non-Smith-first-rank ballots, thus eliminating
some other Smith candidate first. This can lead to that candidate winning.
Alternative Smith *is* an underlying heuristic; while any ISDA method
like Schulze is effectively "eliminate all non-Schwartz candidates and
apply this heuristic" because the heuristic eliminates all non-Schwartz
candidates. The same is true of Ranked Pairs and other ISDA methods.
Schulze and Ranked Pairs have much-more-complex heuristics than Alternative
Smith.
(4) "I am leaning toward Tideman's Alternative Schwartz or Smith
for their simplicity and resistance to tactical voting and nomination."
I don't see why Tideman's alternative methods are supposed to be more
resistant to tactical voting and nomination.
It inherits that from IRV.
http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf
Markus Schulze
----
Election-Methods mailing list - see http://electorama.com/em for list info
----
Election-Methods mailing list - see http://electorama.com/em for list info

----
Election-Methods mailing list - see http://electorama.com/em for list info