- Dear Warren D. Smith,

at your website, you claim that every ranking method violates

either resolvability or reversal symmetry. However, there are

many ranking methods that satisfy both criteria (e.g. the

Schulze method, the Kemeny-Young method, Tideman's ranked

pairs method, and the Borda method).

It is true that it is possible to create examples (like in

the paper by Ivars Peterson) where a concrete ranking method

is indecisive and range voting is decisive. But it is also

possible to create examples where range voting is indecisive

and a ranking method is decisive.

Markus Schulze - --- In RangeVoting@yahoogroups.com, Markus Schulze <markus.schulze@...> wrote:
>

--I do not believe I made that claim. Where?

> Dear Warren D. Smith,

>

> at your website, you claim that every ranking method violates

> either resolvability or reversal symmetry.

> However, there are

--I think you are misunderstanding. (One of) your notions of

> many ranking methods that satisfy both criteria (e.g. the

> Schulze method, the Kemeny-Young method, Tideman's ranked

> pairs method, and the Borda method).

"resolvability" is, in the LIMIT of infinite set of votes each with

some "noise", the probability of a tie goes to zero.

Continuum range voting obeys the far stronger claim that, with ANY

nonempty FINITE set of votes each

with some "noise," the probability of a tie is zero.

This is any advantage of range voting versus, not only Schulze method, but actually versus every ranking-based voting method at all that does not suffer a reversal paradox.

> It is true that it is possible to create examples (like in

--that is misleading. There simply is no probability>0 continuum range voting election

> the paper by Ivars Peterson) where a concrete ranking method

> is indecisive and range voting is decisive. But it is also

> possible to create examples where range voting is indecisive

> and a ranking method is decisive.

> Markus Schulze

(with noisy votes) which is "indecisive."

It is possible to create probability=0 examples -- but who cares? > --I think you are misunderstanding. (One of) your notions of

--another formulation (closer to Schulze's and more precise) is this.

> "resolvability" is, in the LIMIT of infinite set of votes each with

> some "noise", the probability of a tie goes to zero.

>

> Continuum range voting obeys the far stronger claim that, with ANY

> nonempty FINITE set of votes each

> with some "noise," the probability of a tie is zero.

>

> This is any advantage of range voting versus, not only Schulze method, but actually versus every ranking-based voting method at all that does not suffer a reversal paradox.

Schule considers the set of all possible N-voter C-candidate elections. In the limit

N-->infinity with C>0 held fixed.

He shows the Schulze method obeys the property that the proportion of those elections which are tied (indecisive), goes to zero. This is also true of many other voting methods,

for example plain plurality. But there are some methods, such as Copeland, for which this is FALSE. It also is false for "highest median ranking wins."

For continuum range voting, not only does it obey that property, but it obeys the far stronger property, that with N>0 and C>0 BOTH held fixed, the proportion

of possible elections which are indecisive, is zero.

This stronger property is false for Schulze voting. It is also false for every ranking-based voting system which avoids "reversal paradox." It also is false for every ranking-based voting system obeying "neutrality."

One of the problems with the ranking-based voting system crowd, is that they are

so trapped in the "rankings are the only possible kind of vote" false-mindset, that they

don't even notice when somebody points out that entire trap need sot be avoided.

Ranking-based voting voting systems are a design mistake, in my view, and this is one reason why.- At 10:16 AM 3/23/2013, WarrenS wrote:

>Continuum range voting obeys the far stronger claim that, with ANY

This is correct, but a "tie" is not a bad outcome. With Range, and

>nonempty FINITE set of votes each

>with some "noise," the probability of a tie is zero.

with some other methods, it indicates that the electorate is not

ready to make a decision. What to do then is up to special

tie-breaking rules, which can include a coin toss, or, better from

the point of view of majority rule, a runoff.

Warren is here making a strong claim for "continuum range voting,"

which is probably impractical. For those who are not familiar, this

is range with votes being any rational number between 0 and 1 full vote.

>This is any advantage of range voting versus, not only Schulze

I'm unconvinced that this is an advantage. It's a formal rule

>method, but actually versus every ranking-based voting method at all

>that does not suffer a reversal paradox.

satisfaction, for a rule that was just made up. Like a lot of voting

systems criteria, it *sounds* reasonable.

The example given on Warren's page, a generalized HAK election,

generates a tie between the candidates who are mid-preference,

because in order to demonstrate reversal symmetry, it must.

Warren claims that renge voting "solves the problem," but if you

apply the equivalent three-rating range voting, you get an A/K tie.

Condorcet methods produce a three-way tie.

The issue has exposed for me, more clearly, the "assumptions" about

voter preferences that underlie how voting systems work. The behavior

of plurality and IRV assume that voters have a strong preference for

their favorite, and a weak preference -- or no preference -- between

all other candidates. IRV then, when it eliminates a candidate, is

only eliminating a weakly preferred candidate, the harm to election

utility would be small. We, then, analyze IRV with models that do not

satisfy the assumption, and, naturally, IRV fails, badly, and in

real-world situations where this "strong preference for favorite"

don't hold, it has actually held. Plurality essentially has the same

assumption.

IRV *works* in a limited situation which violates the assumption,

that of a minor party spoiler. When this candidate is eliminated,

what is happening is that, if we think of the IRV election as a range

election, the votes for the eliminated candidate are renormalized,

pulling the low assumed rating of the second-ranked candidate for

minor party voters up to one full vote.

Analysis of voting systems has generally ignored runoff voting,

because it's not deterministic from the original ballot set, and it's

messy to analyze, because voters can change their minds with more

information, or simply time to think, and the set of voters in the

runoff may be different than in the primary. Thus an *extremely

common* voting method, that of continuing to vote until a majority

favors an option, is ignored.

Notice that vote-splitting does not affect majority, even when it is

vote-for-one. We have suggested using Approval for runoff voting,

and, strictly speaking, to demonstrate an explicit majority choice,

multiple majorities should *not* be resolved by awarding the win to

the candidate with the most votes. However, that might be done in the

name of efficiency; nevertheless, it introduces possible pathology.

My sense is that a sane method might look at the margin, and go to a

runoff when it is close.

Imagine the HAK election in a vote-for-one top two runoff system. H

does not gain a majority, so there is a runoff. The problem is how to

choose which of A and K goes into the runoff. Whichever one goes into

the runoff -- it might be chosen by lot -- that one, if preferences

are maintained, will win, 2:1, over H. A better primary system would

see that H cannot win a runoff, from the expressed preferences, and

would eliminate H. However, that assumes that the preference

strengths are equal.

I have been suggesting hybrid systems, particularly for use with

majority-required runoff systems, i.e., systems that seek majority

approval and that only terminate in a second election if no majority

can be found, two elections being considered enough.

It's totally clear and should be uncontroversial that a Range or

Score ballot collects the maximum useful information from the voter.

It's been shown -- by Warren -- that with many candidates, Borda is

equivalent to Range, and it's easy to see that a Range ballot is a

ranked ballot with equal ranking allowed. If the resolution is high

enough, a Range ballot can express full ranking. And if a ranked

ballot only allows a limited number of ranks, it likewise involves

equal ranking, at least at the bottom.

Forcing voters to rank candidates when they have no discriminable

preference is introducing noise into the system, and very possibly

bias, especially with relatively unknown candidates. ("I don't like

that name.")

Almost all voting systems set up equal-ranking bottom.

Full-rank-required IRV does not, that's an exception, which would

clearly be rejected in the U.S. (It was rejected when Oklahoma tacked

a second preference requirement into its Bucklin implementation.) So

there is nothing strange about equal ranking, it's just that it's

assumed that this only happens at the bottom. But real voters will

often have *some preference* of a set of voters over full bottom, yet

find it difficult to determine the preference, which indicates that

the set of candidates at that preference level is actually equal --

or close to equal -- in real preference.

A hybrid system can, in two rounds, satisfy the Majority Criterion,

the Condorcet Criterion, and approximate -- closely -- what I'll call

the Range Criterion, i.e., the maximization of expressed social utility.

> > It is true that it is possible to create examples (like in

Sure. Now, see if you can get real voters to vote in a continuum.

> > the paper by Ivars Peterson) where a concrete ranking method

> > is indecisive and range voting is decisive. But it is also

> > possible to create examples where range voting is indecisive

> > and a ranking method is decisive.

> > Markus Schulze

>

>--that is misleading. There simply is no probability>0 continuum

>range voting election

>(with noisy votes) which is "indecisive."

Here is how you could do it: you randomize the votes, i.e, adding a

spread to them over the intermediate range, so if the voter has

voted, say 0.4, the vote is spread over 0.35 - 0.45. But ... this is

equivalent to tossing a coin to resolve a tie in other supposedly

indecisive systems. Add that rule, abe to handle multiple ties, and

they all become decisive. With an open process.

In any case, collecting Range data in elections seems to be something

that could be highly desirable, even if the data is not fully used in

determining the winner.

I've pointed out that the classic Buckln ballot was essentially a

Range 4 ballot over the approved range, with equal rationg bottom for

all canidates, and midrange being considered minimal approval. That

system prohibited multiple voting in ratings 4 and 3, but allowed it

in rating 2. It allowed skipping ratings. It *was* Range, analyzed in

a particular way that looks for a majority, among higher ratings

first, and that completed based on Approval criteria when there was

no majority found.

That system could be improved by

1. Adding the rating value of 1, a disapproved rank/rating, but

preferred over bottom.

2. Allowing equal rating of candidates, which is more realistic and

which can make the system handle more candidates.

3. Holding a runoff when no majority approval can be found.

4. Holding the runoff between, in this order of preference, until two

have been chosen:

A. Range winner.

B. Pairwise winner over the Range winner. If more than one, the

one with the highest total score advances.

(many variations are possible. We have not had much indpendent

analysis of the possibilities.)

5. Allow write-in votes in the runoff, and use an advanced system for

the runoff, like Bucklin, which allows write-in votes in addition to

lower-ranked votes for a named candidate, and can also allow those

who prefer a named candidate to also approve a specific write-in.

From a democratic perspective, majority with repeated ballot, until

majority is found, without eliminations (new nominations, strictly,

with every ballot) is very solid and effective. It's Condorcet

compliant in the final election.

However, it can be made more *efficient*, and that's what Approval

Voting can do, and likewise, even better, Range. A range ballot

provides maximum information to the voters in the next ballot.

We have tended to confuse the generation of information, on which

decisions can be based, with the actual method of making the choice.

Range methods are used all the time, *informally*. Yet for each

person, a decision is made -- or the decision is postponed. People

have a personal threshold for determining Approval cutoff, and they

vary it depending on conditions. Many people will postpone a decision

until circumstances indicate a loss from further delay, in which case

they will lower their approval cutoff until the sense is developed

that one choice is superior, or at least more likely to be superior.

Bucklin, then, with its declining approval cutoff, simulates a series

of repeated elections with declining approval cutoff, quite what

student of Approval have described would happen, as voters become

more intent on generating a result.

So the initial round has minimum approval rating of 4, then it's 3,

then it's 2. This can be pushed toward more detailed rating, and it

can be extended into the unapproved zone, until a Bucklin ballot

becomes a full ranked/rating ballot. (i.e., "full" in the sense that

the entire span of individual perceived utilities is covered.).

We need to distinguish between the ballot system, how voters express

preferences, and the analysis. Obviously analysis can affect voter

strategy, and some analytical methods even encourage reversed

ratings, but when equal rating/ranking is allowed, generally, true

reversal is not needed. There are exceptions with systems that

eliminate candidates, where it may be necessary to Favorite Betray to

allow a better choice in the next round.

But decent systems don't eliminate candidates until a winner is declared. - At 10:39 AM 3/23/2013, WarrenS wrote:

>Ranking-based voting voting systems are a design mistake, in my

If equal ranking and skipped ranks are disallowed, I agree.

>view, and this is one reason why.

Rather than a "mistake," I'd call it a limiting assumption that

disallows a clear expression of preference strength; therefore the

information adequate to begin to estimate the social utility winner is missing.

Ranked methods that disallow equal ranking seem to do so based on the

idea that it's easy for voters to make pairwise choices. That is

something that can be a useful idea, but that fails, under common

circumstances, if equal ranking is prohibited.

Procedurally, voters can clearly rank some candidates over others,

but not necessarily all.

What is weird is that almost all systems allow equal-ranking bottom.

So why not equal ranking at other ranks?

A range ballot does express rankings, if the voter so chooses.

Identical problem, in fact. Do you rate two candidates the same or do

you make a choice, preferring one over the other. With some systems,

strategic considerations will loom large.