[EM] Strategy and Bayesian Regret

[Jameson Quinn]

What makes a single-winner election method good? The primary consideration
is that it gives good results. The clearest way to measure the quality of
results is simulated voter utility, otherwise known as Bayesian Regret (BR).

This is not the only consideration. But for this message, we'll discount the
others, including:

   - Simplicity/voter comprehension of the system itself
   - Ballot simplicity
   - Strategic simplicity
   - Perceived fairness
   - Candidate/campaign strategy incentives


Calculating BR for honest voters is relatively simple, and it's clear that
Range voting is best. But how do you deal with strategy? Figuring out what
strategies are sensible is the relatively easy part; whether it's
first-order rational strategies (as James Green-Armytage has worked
out)
or n-order strategies under uncertainty (as Kevin Venzke does) or even just
simple rules of thumb justified by some handwaving (as in Warren Smith's
original BR work over 10 years ago), we know how to get this far. But once
you've done that, you still have to make some assumptions about how many
voters will use strategy. There are several ways to go about this. In order
of increasing realism, these are:

   1. Assume that voters are inherently strategic or honest and do not
   respond to strategic incentives. Thus, the number of voters using strategy
   will be the same across different systems. Warren Smith's original BR work
   with IEVS seems to have shown that Range is still robustly best under these
   conditions. Although I am not 100% convinced that his definition of strategy
   was good enough, the results are probably robust enough that they'd hold up
   under different definitions.
   2. Avoid the question, and just look at strategic worst cases. I count
   this as more realistic than the above, even though it's just a special case
   of 100% strategy, because it doesn't give unrealistically-precise numbers.
   But of course, if I say that method X has a BR score somewhere between Y and
   Z, and method A has a BR between B and C, if Yhttp://www.econ.ucsb.edu/~armytage/svn2010.pdf>;
it appears that IRV is relatively strategy-resistant, Condorcet is middling,
and Range and Approval are likely to be subject to strategy. But remember,
the whole point of this discussion is that strategy is not so much a problem
in itself, as an input to the model for determining BR. If Approval gives
better results under 100% strategy than IRV does with 0%, then Approval is
still a better system.

Third, there's defensive strategy. Basically, this means looking at the
probability that the result will be subject to strategy from some other
group, and seeing if you can defend against that.

Fourth, there's peer pressure. If you feel that everyone else is
strategizing, you are more likely to do so yourself. This raises the
possibility of positive feedback and multiple equilibria.

It is crucially important to understand that defensive strategy is not like
offensive strategy in terms of peer pressure. If you think that your allies
are unlikely to back you up on your offensive strategy, you may decide it's
pointless to attempt it. But some people will use defensive strategy merely
as insurance. Thus, there is more likely to be a "floor" for defensive
strategy, a certain number of people who use it even if nobody else is. But
it is also true that the more people use strategy, the more people will
worry about defensive strategy. Thus, a method where defensive strategies
are likely to be possible is more likely to be driven to a high-strategy
equilibrium, than one where only offensive strategies are an issue.

So, what does all this mean for BR calculations? Well, first, we should try
to characterize the different systems in terms of the first three factors
above. For the cognitive factor, can we develop some objective measure of
how cognitively difficult it is to work out a good strategy under different
systems? For the offensive strategy factor, we can thank Green-Armytage for
making a good first step in giving the *probability* of strategic
vulnerability, but we should follow up by working out the *amount* of
strategic advantage a voter could expect. For the defensive strategy factor,
Kevin Venzke's work gives some interesting clues, but more work is needed to
isolate defensive factors.

But even once we have all that nailed down, we need a voter model to turn it
into a BR measure for each system. Of course, any such model will be open to
accusations of bias, as it will include varying amounts of strategy under
different voting methods. Range voting advocates in particular might be
motivated to assume that strategy percentage will be the same under
different systems. But it's important to undersand that no assumption here
is unbiased; without real-world data, assuming equal strategy is at least as
biased as a model which accounts for the factors above.

So in the end, I'm inclined to bite the bullet, 

Re: [EM] Strategy and Bayesian Regret

[Andy Jennings]

On Fri, Oct 28, 2011 at 2:43 AM, Jameson Quinn wrote:

> What makes a single-winner election method good? The primary consideration
> is that it gives good results. The clearest way to measure the quality of
> results is simulated voter utility, otherwise known as Bayesian Regret (BR).
>
> This is not the only consideration. But for this message, we'll discount
> the others, including:
>
>- Simplicity/voter comprehension of the system itself
>- Ballot simplicity
>- Strategic simplicity
>- Perceived fairness
>- Candidate/campaign strategy incentives
>
>
> Calculating BR for honest voters is relatively simple, and it's clear that
> Range voting is best. But how do you deal with strategy? Figuring out what
> strategies are sensible is the relatively easy part; whether it's
> first-order rational strategies (as James Green-Armytage has worked 
> out)
> or n-order strategies under uncertainty (as Kevin Venzke does) or even just
> simple rules of thumb justified by some handwaving (as in Warren Smith's
> original BR work over 10 years ago), we know how to get this far. But once
> you've done that, you still have to make some assumptions about how many
> voters will use strategy. There are several ways to go about this. In order
> of increasing realism, these are:
>
>1. Assume that voters are inherently strategic or honest and do not
>respond to strategic incentives. Thus, the number of voters using strategy
>will be the same across different systems. Warren Smith's original BR work
>with IEVS seems to have shown that Range is still robustly best under these
>conditions. Although I am not 100% convinced that his definition of 
> strategy
>was good enough, the results are probably robust enough that they'd hold up
>under different definitions.
>2. Avoid the question, and just look at strategic worst cases. I count
>this as more realistic than the above, even though it's just a special case
>of 100% strategy, because it doesn't give unrealistically-precise numbers.
>But of course, if I say that method X has a BR score somewhere between Y 
> and
>Z, and method A has a BR between B and C, if YX is better than A. So you lose the ability to answer the important
>question, "which method is better?"
>3. Try to use some rational or cognitive model of voters to figure out
>how much strategy real people will use under each method. This is hard work
>and involves a lot of assumptions, but it's probably the best we can do
>today.
>4. Try to get real data about how people would behave in high-stakes
>elections. This is extremely hard, especially because low-stakes polls may
>not be a valid proxy for high-stakes elections.
>
> As you might have guessed, I'm arguing here for method 3. Kevin Venzke has
> done work in this direction, but his assumptions --- that voters will look
> for first-order strategies in an environment of highly volatile polling data
> --- while very useful for making a computable model, are still obviously
> unrealistic.
>
> What kind of voter strategy model would be better? That is, what factors
> probably affect a voters' decision about whether to be strategic? I can
> think of several. I'll give them in order from easiest explanation to
> hardest; the order below has nothing to do with the relative importance.
>
> First, there's the cognitive difficulty of strategizing versus voting
> honestly. In a system like SODA, an honest bullet vote is much simpler than
> a strategic explicit truncation, so we can expect that this factor would
> lead to less strategy. In a ranked system, it is arguably easier to
> strategically exaggerate the perceived frontrunners (Warren's "naive
> exaggeration strategy" or NES) than to honestly rank all the candidates, so
> we might expect this factor to increase strategizing. Note that the
> cognitive burden for strategy is reduced if defensive and offensive
> strategies are the same. For instance, under Range, exaggeration is always a
> good idea, whether it's offensively or defensively.
>
> (Note: This overall cognitive factor is probably most important for "lazy
> voters", and such "lazy voters" are also probably open to strategic and/or
> honest advice from peers, so the cognitive factor is perhaps not too
> important overall.)
>
> Second, there's offensive strategy. The more likely it is that strategy
> will be advantageous against honest opponents, and the more advantageous it
> is likely to be, the more strategy people will use. The first question has
> been addressed by the Green-Armytage 
> paper;
> it appears that IRV is relatively strategy-resistant, Condorcet is middling,
> and Range and Approval are likely to be subject to strategy. But remember,
> the whole point of this discussion is that strategy is not so much a problem
> in itself, as an input to the model for det

Re: [EM] Strategy and Bayesian Regret

[Kristofer Munsterhjelm]

Jameson Quinn wrote:
As you might have guessed, I'm arguing here for method 3. Kevin Venzke 
has done work in this direction, but his assumptions --- that voters 
will look for first-order strategies in an environment of highly 
volatile polling data --- while very useful for making a computable 
model, are still obviously unrealistic.


I can think of another method. It's somewhat unrealistic, but the amount 
of strategy used (and the kind of strategy used) would follow from the 
method itself.


In this method, just consider the election a multiplayer game, and use 
some sort of game AI to model strategy. If you want to use a multiplayer 
generalization of minmax, you'd have to turn the simultaneous game 
turn-based, e.g. the voters go in a random order and can see the votes 
of all those who came before them.


The arbitrary nature of this games-playing approach would be in how you 
model which voters are likely to strategize and how good they are at it 
(perhaps modeled as lookahead). Also, if you consider each possible vote 
a different type of turn and use a tree search like minmax, the approach 
would get impractical very quickly for ranked votes and would probably 
not be feasible at all for rated ones.



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[EM] MMPO and FBC. Votes-only criteria.

[MIKE OSSIPOFF]

(Sorry to change the subject line, but this one is much easier to write.)


Kevin wrote:

Mike's method is Condorcet//MMPO//Condorcet//MMPO//etc.

[unquote]

No. I initially defined such a method. Then I said that I propose only
MMPO (applied to its own ties), because FBC is more important than Condorcet's
Criterion. I said that, as I define MMPO, it _doesn't_ include a CW search, 
because
I want FBC compliance.

I propose MMPO//MMPO//MMPO...

Kevin wrote:

However, even if Mike's method were just MMPO//MMPO//MMPO//etc I
still highly doubt that would satisfy FBC, because the candidate
eliminations and recalculations make it unclear that votes will work
as expected. I don't know how to say this much more clearly than that.
But let me ask you, how many FBC-satisfying methods involve eliminating
candidates and then recalculating scores once those candidates are
removed? Not a one.


[unquote]

I mentioned and answered that argument yesterday on EM.

I'd say it again today, but I don't have long on the computer today. I refer 
you to
my posting yesterday.

Kevin wrote:

Hypothetically, off the top of my head, lowering your true favorite
could remove him from a three-way score tie which then (as a two-way)
is resolved for one of your "other" favorites, whereas the three-way
contest is resolved for a disliked candidate. 

If a compromise (C) could win in a tie, but your favorite (F) couldn't, that 
must
be because C has lower maximum pairwise opposition (MPO) than F.

But, if that's so, then why do you need to vote C over F, to get C into a tie?

I'll be visiting, staying with, relatives this weekend, and I may not get much, 
if any,
time on computers this weekend.  For instance, today there's only time for this 
one posting.

Quinn said that criteria cannot mention sincere preferences.

He neglected to say why he thinks that.

What dictionary is he using?

Look up "criterion". It's a standard for judgment of something. Period.

Someone could say that a votes-only criterion, but not a preferences criterion, 
can be
used to detect noncompliance in an actual election.

Really? What criterion is shown to be violated, by Plurality election results?

Anyway, we don't use criteria in that way, citing actual examples of failure. 
We speak of what _could_
happen. That can be done just as well with criteria that aren't votes-only.

Did you know that Plurality meets the Condorcet Criterion?

It does, if we use a votes-only CC definition.

If for every y not x, more people vote x over y than vice versa, in Plurality, 
then x must win.
Plurality meets votes-only CC.

You might object "But the criterion says "rank" instead of "vote". 

If you vote x over y in a 3-slot ballot, everyone would agree you're ranking x 
over y.

What justification is there for arbitrarily saying that that isn't so with a 
2-slot method such as
Plurality?  In Plurality, you're allowed to rank one candidate over the others.

Look up "rank" in a dictionary. It says what we'd all expect,what rank means to 
us all.

In Plurality, you're ordering one candidate above the others, giving hir a 
higher position than the others.

But if you still want to say that votes-only CC says "rank", and that somehow 
doesn't apply to Plurality, then
you're saying that votes-only CC can't apply to Plurality. Plurality doesn't 
fail it.

Votes-only CC, then, applies only to one class of methods.

You might say that's ok,because we already know we don't like Plurality, and 
none of us are
advocating it. But what about Approval? It, too, meets votes-only CC, unless 
you deny that "voted for" and 
"not voted for" are not different hierarchial levels (ranks). And if you say 
they aren't, then, again,
votes-only CC can't apply to Approval. Can't compare Approval and Condorcet.

My criteria apply seamlessly to all methods, and can compare any and all of 
them to eachother.

Votes-only criteria don't work.

By the way, Plurality meets Minimal Defense too.

Mike Ossipoff






Mike Ossipoff 
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Re: [EM] Strategy and Bayesian Regret

[Kevin Venzke]

Hi Jameson,
 
I am a little short on time, to read this as carefully as I would like, but if 
you have a
moment to answer in the meantime:

--- En date de : Ven 28.10.11, Jameson Quinn  a écrit :
voting is best. But how do you deal with strategy? Figuring out what strategies 
are sensible is the relatively easy part; whether it's first-order rational 
strategies (as James Green-Armytage has worked out) or n-order strategies under 
uncertainty (as Kevin Venzke does) 
 
3. Try to use some rational or cognitive model of voters to figure out how much 
strategy real people will use under each method. This is hard work and involves 
a lot of assumptions, but it's probably the best we can do today.
 

As you might have guessed, I'm arguing here for method 3. Kevin Venzke has done 
work in this direction, but his assumptions --- that voters will look for 
first-order strategies in an environment of highly volatile polling data --- 
while very useful for making a computable model, are still obviously 
unrealistic.
 
[end quotes]
 
I am very curious if you could elaborate on my assumption that voters will 
"look for
first-order strategies in an environment of highly volatile polling data." I'm 
not totally
sure what you mean by first-order vs. n-order strategies, and whether your 
criticism
of unrealism is based on "voters will look for..." part or on the "highly 
volatile polling 
data" part. I wonder if this volatility is a matter of degree or a general 
question of 
approach.
 
I want to note in case it's not clear that when I talk about what strategies 
voters are
using, that is just a reporting mechanism that has awareness of the relationship
between voters' sincere preferences and how they actually voted. The voters have
no idea what they are doing in strategic or sincere terms.
 
Thanks.
 
Kevin
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Re: [EM] MMPO and FBC. Votes-only criteria.

[Jameson Quinn]

2011/10/28 MIKE OSSIPOFF 

>
> (Sorry to change the subject line, but this one is much easier to write.)
>
>
> Kevin wrote:
>
> Mike's method is Condorcet//MMPO//Condorcet//MMPO//etc.
>
> [unquote]
>
> No. I initially defined such a method. Then I said that I propose only
>
> MMPO (applied to its own ties), because FBC is more important than Condorcet's
> Criterion. I said that, as I define MMPO, it _doesn't_ include a CW search, 
> because
> I want FBC compliance.
>
> I propose MMPO//MMPO//MMPO...
>
> Kevin wrote:
>
> However, even if Mike's method were just MMPO//MMPO//MMPO//etc I
> still highly doubt that would satisfy FBC, because the candidate
> eliminations and recalculations make it unclear that votes will work
>
> as expected. I don't know how to say this much more clearly than that.
> But let me ask you, how many FBC-satisfying methods involve eliminating
> candidates and then recalculating scores once those candidates are
>
> removed? Not a one.
>
>
> [unquote]
>
> I mentioned and answered that argument yesterday on EM.
>
> I'd say it again today, but I don't have long on the computer today. I refer 
> you to
> my posting yesterday.
>
> Kevin wrote:
>
> Hypothetically, off the top of my head, lowering your true favorite
> could remove him from a three-way score tie which then (as a two-way)
> is resolved for one of your "other" favorites, whereas the three-way
>
> contest is resolved for a disliked candidate.
>
> If a compromise (C) could win in a tie, but your favorite (F) couldn't, that 
> must
> be because C has lower maximum pairwise opposition (MPO) than F.
>
> But, if that's so, then why do you need to vote C over F, to get C into a tie?
>
> I'll be visiting, staying with, relatives this weekend, and I may not get 
> much, if any,
> time on computers this weekend.  For instance, today there's only time for 
> this one posting.
>
> Quinn said that criteria cannot mention sincere preferences.
>
>
What I meant was, if a criterion says system X must give result Y for
ballots Z and sincere preferences Q, then it also says that X must give Y
for Z and R. As long as there is some Q for which (Q,Z) meets the criterion,
then Z meets the criterion for any preferences. This is just what a voting
system is; if it gives Y for (Q,Z), it gives Y for (Q,R), unless it can read
minds.

JQ

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Re: [EM] Strategy and Bayesian Regret

[Jameson Quinn]

2011/10/28 Kevin Venzke 

> Hi Jameson,
>
> I am a little short on time, to read this as carefully as I would like, but
> if you have a
> moment to answer in the meantime:
>
> --- En date de : *Ven 28.10.11, Jameson Quinn * a
> écrit :
>
> voting is best. But how do you deal with strategy? Figuring out what
> strategies are sensible is the relatively easy part; whether it's
> first-order rational strategies (as James Green-Armytage has worked 
> out)
> or n-order strategies under uncertainty (as Kevin Venzke does)
>
> 3. Try to use some rational or cognitive model of voters to figure out how
> much strategy real people will use under each method. This is hard work and
> involves a lot of assumptions, but it's probably the best we can do today.
>
>
> As you might have guessed, I'm arguing here for method 3. Kevin Venzke has
> done work in this direction, but his assumptions --- that voters will look
> for first-order strategies in an environment of highly volatile polling data
> --- while very useful for making a computable model, are still obviously
> unrealistic.
>
> [end quotes]
>
> I am very curious if you could elaborate on my assumption that voters will
> "look for
> first-order strategies in an environment of highly volatile polling data."
> I'm not totally
> sure what you mean by first-order vs. n-order strategies,
>

First-order strategies are strategies which work assuming all other
factions' votes are unchanged. Second-order strategies either respond to, or
defend against, first-order strategies. I guess that your system, through
iterated polling, deals with "respond to", but it is incapable of "defend
against".


> and whether your criticism
> of unrealism is based on "voters will look for..." part or on the "highly
> volatile polling
> data" part.
>

Some of the former (lack of defense), but mostly the latter.

Also, it's not so much a criticism, as a pointer for what comes next. You
have *absolutely* gone farther than anyone else I know of in exploring the
motivators and consequences of strategy across voting systems, and if my
appreciation of that fact didn't come through, I'm sorry. (Green-Armytage
has some answers you don't about motivators, and Smith's IEVS has some about
consequences, but your work is by far the best for combining the two.)


> I wonder if this volatility is a matter of degree or a general question of
> approach.
>

Well, I've never seen you try to justify the volatility in terms of realism.
It's a computational trick, to prevent excessive equilibrium, from what I
can tell. That is, your unrealistic (perfectly rational in some ways but
utterly lacking in any meta-rationality) voters may need this unrealistic
assumption to give more-realistic answers, and if so, then "fixing" this one
issue is not the answer. (If there were no volatility, I think that your
system would end up comparing a lot of 100%/0% numbers, which doesn't
discriminate very well between systems.)


>
> I want to note in case it's not clear that when I talk about what
> strategies voters are
> using, that is just a reporting mechanism that has awareness of the
> relationship
> between voters' sincere preferences and how they actually voted. The voters
> have
> no idea what they are doing in strategic or sincere terms.
>

Yes, I understand that.

Cheers,
Jameson

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Re: [EM] question about Schulze example (A,B,M1,M2)

[Markus Schulze]

Hallo,

as long as the used tie-breaking strategy guarantees
that M1 is ranked ahead of M2, I see no problem.
See section 5 of my paper:

http://m-schulze.webhop.net/schulze1.pdf

Markus Schulze


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Re: [EM] question about Schulze example (A,B,M1,M2)

[capologist]

> See section 5 of my paper:

Not quite what I'm looking for. That section describes a non-deterministic 
method for generating a complete linear order.

I don't require a linear order. I'm OK with a partial ordering.

I'm looking for a deterministic method for generating a "picture" (partial 
ordering) of how the voters, in aggregate, feel about the preferability of the 
available options.  (What we're doing at this stage is more akin to a poll than 
an election.)  It seems to me that the A>(M1,M2)>B ordering does not reflect 
the voters' preferences as well as the A>M1>M2>B ordering.

I'm open to the possibility that the Schulze method is the wrong tool for this 
purpose.

I'm also open to the possibility that the Schulze method is the right tool for 
this purpose, and is serving that purpose effectively in this scenario. That 
would imply that, in some meaningful sense, A>(M1,M2)>B is at least as good or 
a better picture of the voters' preferences than A>M1>M2>B. This is 
counterintuitive but perhaps it makes sense and I don't yet understand why.

I think the latter is likely the case. M1 and M2 are beatpath tied. What's 
going on in this example is that there is a beatpath of strength at least 2 
(using margins) from every candidate to every candidate. Since M1's pairwise 
win over M2 is not stronger than this value, it has no effect. Is this a case 
of a meaningful but weak signal being lost in "noise"? Or is the strength-2 
cycle itself a meaningful signal that, for good if inscrutable reason, 
overrides the weak preference between the clones?


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Re: [EM] Results for Poll for Favorite Single-Winner Voting System

[Richard Fobes]

On 10/25/2011 11:08 PM, ⸘Ŭalabio‽ wrote:

¡Thanks for telling us about the poll after it concludes!  The winner, 
IRV, is 1 of the worst voting systems.  The best choice in the poll is Approval 
Voting.



The survey results (with the raw ballot info copied below) reveal that 
IRV supporters "stuffed" the ballot box.


I've learned from public surveys that the best-networked voters -- the 
ones who tell other fans of the same choice(s) to vote in a survey -- 
can easily out-vote the fans of other choices.


(With this kind of bias I figure it's not worth calculating 
Condorcet-Kemeny ranking results.)


Richard Fobes


9 1
(0) 1 1 3 9 5 6 4 0
(1) 1 3 8 1 5 7 6 2 4 0
(2) 1 9 4 1 5 0
(3) 1 1 3 0
(4) 1 6 3 7 1 8 5 4 9 2 0
(5) 1 3 9 8 6 5 1 2 4 7 0
(6) 1 1 9 4 8 7 3 5 2 6 0
(7) 1 7 1 3 5 6 4 0
(8) 1 3 1 2 8 4 7 9 5 6 0
(9) 1 1 7 3 9 4 5 8 2 6 0
(10) 1 1 0
(11) 1 9 1 5 0
(12) 1 1 3 7 4 9 6 8 5 2 0
(13) 1 1 6 3 5 0
(14) 1 9 1 3 5 0
(15) 1 1 3 4 9 6 5 7 8 2 0
(16) 1 5 0
(17) 1 1 3 9 0
(18) 1 3 5 6 1 7 8 4 9 0
(19) 1 9 8 5 3 6 1 7 2 4 0
(20) 1 3 1 8 7 6 4 9 5 2 0
(21) 1 1 3 6 0
(22) 1 1 4 3 0
(23) 1 5 0
(24) 1 3 1 5 2 0
(25) 1 1 7 3 2 0
(26) 1 6 5 8 3 0
(27) 1 1 3 5 0
(28) 1 3 1 9 5 6 8 2 4 0
(29) 1 1 3 6 0
(30) 1 9 5 6 8 3 7 4 1 2 0
(31) 1 5 0
0
"Instant runoff voting"
"Plurality voting"
"Condorcet voting"
"Borda count"
"Approval voting"
"Range voting"
"Coombs method"
"Bucklin system"
"Other"
"Favorite single-winner voting system"


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Re: [EM] question about Schulze example (A,B,M1,M2)

[Richard Fobes]

FYI, the Condorcet-Kemeny method correctly ranks M1 as second-most 
popular, and M2 as third-most popular.  And it does so without the need 
for a "tie-breaker" adjustment.


Richard Fobes

On 10/27/2011 8:46 PM, capologist wrote:

I recently conducted a vote under the Schwartz method. It produced a
result that is counterintuitive and that I don’t know how to justify.

Here’s a simplified version of the scenario:

*5x A > M1 = M2 > B*
*3x B > A > M1 = M2*
*2x M1 = M2 > B > A*
*2x M1 > M2 > B > A*

The partial ordering produced by the Schulze method has *A* beating
everybody else, *B* losing to everybody else, and *M1* and *M2* “tied”
in the middle:


The question regards the clone pair *(M1, M2)*. Why shouldn’t *M1* be a
winner over *M2*? Nobody would object to that. Some voters would prefer
it, and the rest don’t care one way or the other.

I don’t know how to explain to the voters who prefer *M1* over *M2* why
their preference shouldn’t be reflected in the results when nobody
disagrees with it.




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Re: [EM] question about Schulze example (A,B,M1,M2)

[Markus Schulze]

Hallo,

> Not quite what I'm looking for. That section describes
> a non-deterministic method for generating a complete
> linear order.

Well, although this tie-breaking strategy is _formulated_
as a random tie-breaker, it is almost always decisive.

Markus Schulze


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