[EM] Another Proposed Single-winner Method

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[EM] Another Proposed Single-winner Method

William WAUGH
Goals

My design goals here are:

1. The election method I am proposing must (like Score Voting) remove the strategic need for candidates to expensively convince voters they are one of the "2 most likely to win".

2. The method should be perceived to provide the perceived benefit of IRV over Score, at least as well as IRV is perceived to, that a voter can support a compromise candidate without diluting the voter's support for the voter's favorite candidate.

To obtain the above two benefits, I am willing to accept the following costs:

- The method need not be precinct-summable.

Grammar of the Ballot

The voter fills the ballot with an ordered list of stanzas.

Each stanza lists a candidate or some candidates.

Furthermore, each stanza is marked "Interpretation Category A" or "Interpretation Category B". The default is "A".

Procedure for the Tally

As a preliminary step for the tally, the tallying agent must scan the ballots to collect the names written in. Then the candidate set is initialized to include all the written-in names.

The tallying proceeds in rounds.

Each round receives as an argument, a set of candidates who are said to be "still in the running". For the first round, this is the entire set of candidates.

Each round uses a set of accumulators. One accumulator is associated to each candidate who is still in the running. At the start of the round, these accumulators are initialized to zero.

The next step for executing the round of tallying requires going through the ballots, visiting each one.

The first step during a visit to a ballot in the context of a round of tallying is to scan down the stanzas on the ballot to find the first one that applies to the current set of candidates still in the running.

If a stanza is marked for interpretation category "A", such a stanza applies if and only if any of the candidates named in the stanza is still in the running.

Otherwise, the stanza applies if and only if and only if any of the candidates who were in the full candidate set at the start of the tally who are not named in the stanza is still in the running.

The accumulator associated to each candidate named in the stanza (if the candidate is still in the running) is incremented by one. Once this is done based on this one stanza, the procedure for the round of tallying proceeds to the next ballot.

When the procedure for the round of tallying has visited all the ballots, said procedure carries out the summing-up of the round, as follows.

Halve the count of the candidates remaining in the running. If the result is not a whole number, round it down to the next lower whole number. So for example, if there are three candidates in the running, half that is 1 1/2, and we round that down to 1. The rounded-down result is the count of candidates who have to be eliminated from the running by this round of the tally. Eliminate the that-many candidates having the lowest values in their accumulators.

After elimination, if only one candidate remains, yield that candidate as the winner.

Otherwise, proceed to the next round of tallying, using the not-eliminated candidates as the candidates in the running for that next round.

Questions

1. Can you point out a simpler election method that you think would work at least as effectively as the one I propose above, to unseat oligarchy? (Score Voting is simpler, since it is precinct-summable).

Analysis

You may be wondering why I included the possibility for the voter to choose Interpretation Category "B". No doubt when you first read it, it sounded strange and arbitrary.

I believe that in order to remove the strategic need for candidates to expensively convince voters they are one of the "2 most likely to win", an election method must meet two constraints:

1. Frohnmayer balance; and

2. Sufficient expressivity.

I don't know where to draw the line for sufficiency of expressivity, but I think the above proposed method does have sufficient expressivity, and I think that vote-for-and-against and vote-for-or-against (a. k. a. Negative Vote) don't.

Frohnmayer balance means that every vote that can be cast in the system has an antivote. "Antivote" means a vote such that if the original vote and its antivote are entered in the election, the winner is the same as though neither the original vote nor its antivote had been entered.

The choice between the two interpretation categories I provide for stanzas permits me to construct for any given vote its antivote.

Starting with the original vote, we construct its antivote stanza by stanza. Each stanza in the antivote corresponds to the stanza in the same position in sequence in the original vote. The antistanza of a given stanza uses the opposite interpretation category and names the complement of the set of candidates named by the original stanza under the complete set of candidates in the election QED

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Re: [EM] Another Proposed Single-winner Method

Kristofer Munsterhjelm-3
On 17/04/2019 09.53, William WAUGH wrote:

> *Goals*
>
> My design goals here are:
>
> 1. The election method I am proposing must (like Score Voting) remove
> the strategic need for candidates to expensively convince voters they
> are one of the "2 most likely to win" <https://rangevoting.org/Cash3.html>.
>
> 2. The method should be perceived to provide the perceived benefit of
> IRV over Score, at least as well as IRV is perceived to, that a voter
> can support a compromise candidate without diluting the voter's support
> for the voter's favorite candidate.
>
> To obtain the above two benefits, I am willing to accept the following
> costs:
>
> - The method need not be precinct-summable.

[snip]

> *Questions*
>
> 1. Can you point out a simpler election method that you think would work
> at least as effectively as the one I propose above, to unseat oligarchy?
> (Score Voting is simpler, since it is precinct-summable).

A Condorcet perspective:

If a candidate is inside the Smith-set, it is well known, otherwise it
would be beaten by most of the other candidates (either by not being
ranked, or by being ranked below them on a majority of the ballots).
Thus, any election method that passes ISDA ensures that unknown parties
or candidates can't change the outcome.

In other words, there's no need for a candidate to use a lot of money
convincing the voters that he's very important and that voting for him
will not be a waste, because:

- either he's not in the Smith set, and the method passes ISDA, so it
doesn't matter where the voter ranks him, or

- he's in the Smith set, in which case he's well known already and
doesn't need huge amounts of money to promote himself.

More broadly, in FPTP/Plurality, it's important for a candidate to
signal that he's one of the frontrunners because voting for someone who
is not a frontrunner may make the wrong frontrunner win. This is called
compromise incentive: voting for a frontrunner even though you like some
non-frontrunner better is "compromising" for that frontrunner.

James Green-Armytage's paper, "Strategic Voting and Nomination" (e.g.
https://mpra.ub.uni-muenchen.de/32200/1/MPRA_paper_32200.pdf ) shows
that Condorcet methods generally have very low compromising incentive,
and so that won't be a problem.

In all fairness, I should say that the classical Condorcet methods
(Schulze, MAM/RP, etc.) are susceptible to burial. A follow-up paper of
Green-Armytage's, "Four condorcet-hare hybrid methods for single-winner
elections" (e.g.
https://pdfs.semanticscholar.org/49db/a225741582cae5aabec6f1b5ff722f6fedf1.pdf),
shows that Condorcet-IRV hybrids resist burial pretty well, albeit at
the cost of monotonicity and precinct summability.
Burial might not matter, and in that case, MAM/RP or Schulze is good
enough (and is at least somewhat known). But if burial resistance is
important to deter two-party rule, then use Hare (IRV) hybrids instead.

(Incidentally, I'm currently working on finding a method that is
monotone, passes ISDA, and that resists both burial and compromising.)

It's also possible to argue that all forms of election will result in
some sort of rule by the few. I've ignored that here, because getting
into a discussion of how few are too few would distract from the point
above.

> *Analysis*
>
> You may be wondering why I included the possibility for the voter to
> choose Interpretation Category "B". No doubt when you first read it, it
> sounded strange and arbitrary.

I suspect that the voters will have the same thought. Suppose the
proposed method, when properly used, does what you say it does (that is,
stops oligarchy). Then the ballot format would probably still lead the
voters to scratch their heads going "what's all this stanza and
interpretation category business?". It's not particularly user-friendly.

It might be better suited as a multiple round runoff method. In each
round of the runoff, the voters know precisely who are in the running,
and there's no need for the contingency options of the stanzas and
interpretation categories.

> I believe that in order to remove the strategic need for candidates to
> expensively convince voters they are one of the "2 most likely to win"
> <https://rangevoting.org/Cash3.html>, an election method must meet two
> constraints:
>
> 1. Frohnmayer balance; and
>
> 2. Sufficient expressivity.

Random ballot seems to be a counterexample to both of these. Random
ballot uses Plurality-style ballots, and so is neither expressive nor
has the balance property. Yet it is completely strategy-proof. Either
your ballot is chosen to determine the winner or it isn't; if it's
isn't, it doesn't matter what you put on it, and if it is, you're best
off by putting your favorite first. Thus, there's no need for a
candidate to claim to be a frontrunner, because compromising strategy is
pointless.

Asset could also serve as a counterexample to sufficient expressivity,
if the candidates are sufficiently good at negotiating. (Perhaps party
list PR democracies also fit here, but maybe the system is too different
for the constraints to apply.)

The Condorcet-Hare hybrids also resist both burial and compromising, yet
clearly fail Frohnmayer balance since IRV itself fails it.

From the other end, I doubt the following method is immune to
vote-splitting, even though it obeys both constraints:

- Each voter rates each candidate between 0 and 10, and marks his ballot
either "+" or "-".
To count a ballot:
        - The ballot is normalized so that the sum of scores is 1.
        - If the mark is "+", then for each candidate A, the normalized
ballot's score for A is added to A's total. If the mark is "-", the
normalized ballot's score for A is subtracted.

This is basically cumulative voting with Range ballots, and with a tweak
to make it satisfy 1. Continuous cumulative voting has a serious
vote-splitting problem where the best strategy is to give the preferred
frontrunner 10 and everybody else 0. I don't think adding a subtraction
option removes that incentive.
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[EM] Single-winner Methods Empower Few?

William WAUGH
On Wed, Apr 17, 2019 at 7:42 AM Kristofer Munsterhjelm wrote:
...
It's also possible to argue that all forms of election will result in
some sort of rule by the few. I've ignored that here, because getting
into a discussion of how few are too few would distract from the point
above.

Which few would rule if the form were Score Voting? 

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Re: [EM] Single-winner Methods Empower Few?

Kristofer Munsterhjelm-3
First of all, this did end up later than I wanted. Other things have
been occupying my time, and though I've wanted to give a better account
than I have below, I think it's been long enough.

Second, the random selection I contrast to elections below more or less
forces some kind of multiwinner system, because otherwise the variance
would be unacceptable. You can't randomly select a president (well, you
could, but it wouldn't be a good idea to leave that much to chance).

(But on the flipside, that means the argument against elections isn't
just applicable to single-winner, but to multi-winner/PR as well.)

On 18/04/2019 13.06, William WAUGH wrote:

> On Wed, Apr 17, 2019 at 7:42 AM Kristofer Munsterhjelm wrote:
>
>     ...
>     It's also possible to argue that all forms of election will result in
>     some sort of rule by the few. I've ignored that here, because getting
>     into a discussion of how few are too few would distract from the point
>     above.
>
>
> Which few would rule if the form were Score Voting?

The short answer is: the politicians. If the system is good, the
politicians will be those who are better at governing; if not so good,
the politicians will be a group of people who are able to use their
preexisting power to control the method and the voters more effectively
than the method and the voters can control them.

The point of an election method is to find the best of a number of
alternatives. Inherent in the use of elections to begin with is that
determining who is the best is a difficult task, i.e. that not all the
contenders are well-suited. If all were well enough suited on average,
you could just do what polling organizations do: choose a number of them
at random (after compensating for chance).

For the classical argument, it's probably easiest to refer to the
ancient Greeks. When analyzing forms of government, Aristotle divided
them into three types (rule by one, rule by a few, and rule by many),
and furthermore into two categories based on whether the rulers only
ruled for their own benefit, or for the benefit of people at large. He
called self-serving rule by few oligarchy, and rule by few for the
benefit of the people, aristocracy. He then argued that elections lead
to some form of rule by few or a minority, i.e. to aristocracy or
oligarchy (for, as I understand it, a reason similar to what I said above).

One might argue that a rule of the skilled or extraordinarily able is a
good form of rule by a minority. That may be so, but it is nevertheless
a rule by a minority. Such an argument is, in effect, saying that
there's no problem with a rule by few; the problem is when that rule
becomes an oligarchy rather than an aristocracy. If one has no problem
with aristocracy *as such*, then keeping the system from degrading into
oligarchy is of course very important. Better election method contribute
to this by making it much harder for the rulers to twist the criteria by
which they're judged to something that favors themselves rather than the
voters.

But one could still have objections to all kinds of rule by a minority,
however effective or selfless. From what I understand, the Athenians
considered equality of power (that everybody have the same chance to be
part of the governing mechanism) as an extension of equality under the
law, and thus a right that citizens should have. If aristocracy is more
effective than democracy, that doesn't matter. It's analogous to the
thought that even if authoritarianism is more effective than
(representative) democracy and gets the trains running on time,
democracy is preferrable because people should govern themselves.

Alternatively, one could argue that education and wisdom of crowds make
sufficiently large random assemblies not that much worse than elected
assemblies, to the point where one loses more to the risk of corruption
(sliding into oligarchy) by going with elections than one loses by
mediocrity (so to speak) by going with random selection. The more
effective mechanisms like deliberative polls are, the stronger that
argument is. And the more oligarchy-resistant electoral democracy is
with good election methods, the weaker the argument.
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Re: [EM] Single-winner Methods Empower Few?

Abd ul-Rahman Lomax
The Iron Law of Oligarchy is very strong, but key to democracy is
*consent.* If the people consent to rule by a few, it is still
oligarchy, but an oligarchy serving the people. I suppose Aristotle
would call that aristocracy.

The minimum level of consent is majority. A higher level of consent will
generally lead to a stronger society, but my experience with "consensus
rules" is that they lead to domination by a minority whenever the status
quo favors them. Hence what I propose is the establishment of strong
tradition for respect for the rights of minorities, without going so far
as to remove power from the majority to decide the limits of power.

In practical democratic rules for deliberative process, these rights are
protected extensively, preventing a mere majority from steamrollering a
significant percentage of members. For example, a motion for the
Previous Question (called "cloture" in the U.S. Senate) requires a 2/3
vote of those present under Robert's Rules. (The Senate reduced that to
60%, and the "nuclear option" uses another democratic loophole: an
absolute majority of eligible voters -- the members -- can amend the
rules at any time. This is the power of a majority, and it is causing
much division because of the increasing power of political parties.

Asset Voting could demolish the dependence on political parties, by
creating a *fully representative* Electoral College which would then
elect an Assembly, each seat being elected by unanimous agreement of
electors holding a quota of votes. When we think of Asset under the
present system, we think of ballots with a limited number of candidates
on them, and ballot access is dominated by parties, but since Asset
wastes no votes, it would no longer be necessary to vote strategically,
sane strategy simply becomes "vote for whomever you trust most," and I
add, generally, "and whom you can personally meet." There could be many
thousands of those registering to be public voters.

Asset will be strongly opposed, it can be expected, by political
parties, by media, and by everyone who benefits from the existing
election system.

Hence I suggest Asset be first implemented in NGOs, because until people
experience it, those forces will convince people that this is a
dangerous reform that will destroy everything we love and create all we
hate.

Score voting is a nice reform, though there is even better (i.e., runoff
voting with score ballots; most voting system reform people have
completely missed the requirement for a majority approval for election,
which was basic democracy.) Approval is the simplest voting reform,
simply Count All The Votes, don't discard multiple votes. But this will
not fundamentally change the system. Asset would.

Not only will there exist a fully representative Assembly, with seats
chosen, not "elected in a contest," but there will also exist an
intermediate body, providing visible communication channels between the
public and the seats, i.e,. the Electoral College, the body of electors,
public voters, so the seats know who elected them (and the public knows
who it voted for, so they will see the actual power resulting from their
vote, even though the electors will not necessarily know who voted for
them.)

On 4/29/2019 6:08 PM, Kristofer Munsterhjelm wrote:

> First of all, this did end up later than I wanted. Other things have
> been occupying my time, and though I've wanted to give a better account
> than I have below, I think it's been long enough.
>
> Second, the random selection I contrast to elections below more or less
> forces some kind of multiwinner system, because otherwise the variance
> would be unacceptable. You can't randomly select a president (well, you
> could, but it wouldn't be a good idea to leave that much to chance).
>
> (But on the flipside, that means the argument against elections isn't
> just applicable to single-winner, but to multi-winner/PR as well.)
>
> On 18/04/2019 13.06, William WAUGH wrote:
>> On Wed, Apr 17, 2019 at 7:42 AM Kristofer Munsterhjelm wrote:
>>
>>      ...
>>      It's also possible to argue that all forms of election will result in
>>      some sort of rule by the few. I've ignored that here, because getting
>>      into a discussion of how few are too few would distract from the point
>>      above.
>>
>>
>> Which few would rule if the form were Score Voting?
> The short answer is: the politicians. If the system is good, the
> politicians will be those who are better at governing; if not so good,
> the politicians will be a group of people who are able to use their
> preexisting power to control the method and the voters more effectively
> than the method and the voters can control them.
>
> The point of an election method is to find the best of a number of
> alternatives. Inherent in the use of elections to begin with is that
> determining who is the best is a difficult task, i.e. that not all the
> contenders are well-suited. If all were well enough suited on average,
> you could just do what polling organizations do: choose a number of them
> at random (after compensating for chance).
>
> For the classical argument, it's probably easiest to refer to the
> ancient Greeks. When analyzing forms of government, Aristotle divided
> them into three types (rule by one, rule by a few, and rule by many),
> and furthermore into two categories based on whether the rulers only
> ruled for their own benefit, or for the benefit of people at large. He
> called self-serving rule by few oligarchy, and rule by few for the
> benefit of the people, aristocracy. He then argued that elections lead
> to some form of rule by few or a minority, i.e. to aristocracy or
> oligarchy (for, as I understand it, a reason similar to what I said above).
>
> One might argue that a rule of the skilled or extraordinarily able is a
> good form of rule by a minority. That may be so, but it is nevertheless
> a rule by a minority. Such an argument is, in effect, saying that
> there's no problem with a rule by few; the problem is when that rule
> becomes an oligarchy rather than an aristocracy. If one has no problem
> with aristocracy *as such*, then keeping the system from degrading into
> oligarchy is of course very important. Better election method contribute
> to this by making it much harder for the rulers to twist the criteria by
> which they're judged to something that favors themselves rather than the
> voters.
>
> But one could still have objections to all kinds of rule by a minority,
> however effective or selfless. From what I understand, the Athenians
> considered equality of power (that everybody have the same chance to be
> part of the governing mechanism) as an extension of equality under the
> law, and thus a right that citizens should have. If aristocracy is more
> effective than democracy, that doesn't matter. It's analogous to the
> thought that even if authoritarianism is more effective than
> (representative) democracy and gets the trains running on time,
> democracy is preferrable because people should govern themselves.
>
> Alternatively, one could argue that education and wisdom of crowds make
> sufficiently large random assemblies not that much worse than elected
> assemblies, to the point where one loses more to the risk of corruption
> (sliding into oligarchy) by going with elections than one loses by
> mediocrity (so to speak) by going with random selection. The more
> effective mechanisms like deliberative polls are, the stronger that
> argument is. And the more oligarchy-resistant electoral democracy is
> with good election methods, the weaker the argument.
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
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Re: [EM] Single-winner Methods Empower Few?

Kristofer Munsterhjelm-3
On 03/05/2019 00.06, Abd ul-Rahman Lomax wrote:
> The Iron Law of Oligarchy is very strong, but key to democracy is
> *consent.* If the people consent to rule by a few, it is still
> oligarchy, but an oligarchy serving the people. I suppose Aristotle
> would call that aristocracy.

Consent doesn't need to lead to something that serves the people.
Suppose e.g. there's a Kodos and Kang scenario and the voters have grown
so used to FPTP that they can't think of an alternative. They might
consent to the lesser evil, but neither space alien would serve the people.

> The minimum level of consent is majority. A higher level of consent will
> generally lead to a stronger society, but my experience with "consensus
> rules" is that they lead to domination by a minority whenever the status
> quo favors them. Hence what I propose is the establishment of strong
> tradition for respect for the rights of minorities, without going so far
> as to remove power from the majority to decide the limits of power.

Jobst Heitzig once detailed an interesting variant on consensus rule:
everybody designates a consensus choice and a favorite. If enough of the
members choose the same consensus choice, then that option wins,
otherwise a random favorite is chosen.

The point of choosing a random favorite is that random ballot is both
strategyproof and unbiased. Since random ballot is not a particularly
good method beyond having these features, it provides an incentive for
some supermajority to agree on the consensus option.

(Jobst originally suggested the supermajority be unanimity, but there's
nothing stopping anyone from using "just" a supermajority.)

> In practical democratic rules for deliberative process, these rights are
> protected extensively, preventing a mere majority from steamrollering a
> significant percentage of members. For example, a motion for the
> Previous Question (called "cloture" in the U.S. Senate) requires a 2/3
> vote of those present under Robert's Rules. (The Senate reduced that to
> 60%, and the "nuclear option" uses another democratic loophole: an
> absolute majority of eligible voters -- the members -- can amend the
> rules at any time. This is the power of a majority, and it is causing
> much division because of the increasing power of political parties.
>
> Asset Voting could demolish the dependence on political parties, by
> creating a *fully representative* Electoral College which would then
> elect an Assembly, each seat being elected by unanimous agreement of
> electors holding a quota of votes. When we think of Asset under the
> present system, we think of ballots with a limited number of candidates
> on them, and ballot access is dominated by parties, but since Asset
> wastes no votes, it would no longer be necessary to vote strategically,
> sane strategy simply becomes "vote for whomever you trust most," and I
> add, generally, "and whom you can personally meet." There could be many
> thousands of those registering to be public voters.

In your other post, you gave an example of a nation of a million with 1%
of the voters being electors, and you furthermore said that Asset is
deliberation and negotiation.

That is one thing I've always found strange about Asset. How are you
going to get ten thousand people in a room to negotiate? (Or even "on
the internet to negotiate".) I imagine that the same quadratic scaling
problem that burdens direct democracy would come into play here too
unless there is some kind of shortcut that can be made.

But those shortcuts could well introduce serious path dependence into
the negotiation process itself. That's the kind of thing that makes IRV
behave so chaotically.
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