[EM] Ranked Preferences, example calculations

[Abd ul-Rahman Lomax]

At 09:13 AM 10/29/2006, Chris Benham wrote:
>CB: No.I see "group decision making process" as spread out along a 
>continuum with "informal consensus"
>at one end and civil war or violent "mob rule" at the other. Abd 
>sees elections as (in his view undesirably)
>substituting for consensus and wants to change them into mechanisms 
>for reaching a formal consensus,
>whereas I think they should more properly be seen as tough 
>competitions that substitute for civil war.

I do not agree with Chris's characterization of my position. For 
example, I believe that the majority has the right of decision. The 
majority can and should decide what level of public approval is 
required before going ahead. But the majority should be an informed majority.

Mass electoral systems don't do this. And poor election methods don't 
*substitute* for civil war, they can lead to civil wars, and have.

>A group of people ordering pizza are presumably a freely associating 
>group of friends, so all are
>considerate of the other's strong preferences (and "needs") and 
>no-one wants to oppress  anyone  or
>listen to anyone whingeing while they are trying to enjoy their pizza.

Of course, society is, instead, a bunch of people who don't care 
about each other, are inconsiderate of the strong preferences of 
anyone but themselves, want to oppress anyone who they find 
inconvenient, and loves to listen to whining because they hate anyone 
different from them.

What a vision, Chris!

>  (And of course if anyone is really unhappy
>they can presumably just leave the group and not starve.)So in that 
>case of course the group would
>probably quickly come to an informal consensus, and if there *was* 
>any formal "voting" then I suppose
>some variation of  Range or Approval would do and may be best.

It's called "deliberative process," if they care to become formal 
about it, and we know really well how to do it in small groups. The 
*only* difference between this and a large society should be the 
scale. The problem is that classic deliberative process does not 
scale well. Delegable Proxy was invented to deal with the problem of 
scale; it essentially reduces the large scale to a small one; this is 
the same solution as representative democracy, except that Delegable 
Proxy, or its cousin Asset Voting, don't exclude minorities from 
participation in deliberation. Just as minorities are not excluded in 
small-scale direct democracies, such as Town Meeting.

Now, if Range or Approval is best for small groups that care about 
each other, at what point does this superiority disappear? Where is 
the transition between the Range Good region and the Neglect 
Preference Strength region?

If Neglect Preference Strength is clearly a bad idea when the scale 
is small, why does it become a good idea when the scale is large? 
What is the cause of this alleged shift?

>But suppose in an experiment to please Abd, the pizza orderers 
>aren't friends and maybe even dislike
>each other, they are very hungry and there won't be enough pizza to 
>satisfy everyone's hunger and the
>people are locked in the room with nothing to eat but this pizza 
>they are ordering.

Aha. Zero-sum game. Neglect Preference in a zero-sum game, where 
people are fighting over scarce resources and if I win, you lose, or 
if you win, I lose.

>  Then "informal consensus"
>will tend to break down and we will have a scenario more appropriate 
>for a tough election. Voters might
>have incentive to vote for a variety others dislike in the hope they 
>will then get a bigger share.

This is Chris's vision of society: a dog-eat-dog, vicious 
competition, don't-care-about-them world.

Let's just say that I don't see the world that way. And if I did, 
well, there is always what wilderness is left. I would not be working 
on improved organizational techniques if I thought that people were 
intrinsically the way that Chris sees them. I'm trying to build 
systems that will bring out the best in people, not the worst.

Yes, people can be mean and vicious. They can be greedy and, yes, 
stupid. And I'm a person myself. But, in some words I wrote quite a 
while ago, I was not born for this, I did not drink milk for this.


>>Essentially, some writers treat the vulnerability of Range to
>>strategic voting as if it were a proven thing. They simply assume it.
>>It has *not* been proven, far from it. And it seems to me that this
>>is a false charge against Range.
>>
>>
>It would. It is obvious to anyone with a clue that it is.

Okay, Warren, are you reading this? Is what Chris is saying true? 
Anyone else who is knowledgeable about Range Voting agree with Chris? 
I know that the charge is often made, and sometimes Range advocates 
will say something that admits the alleged strategic voting 
vulnerability, but I have *never* seen a clear discussion of this.

Chris's argument here is thoroughly offensive. He is essentially 
saying, "I don't have to substantiate the charge, it is obvious, 
anybody knowledgeable knows it. However, he *does* go on to present 
what he claims is evidence. Let's look at it.

>>>The problem with Range is that if  "the majority" are not self-aware
>>>and coordinated, they cannot
>>>"easily get what they want".
>>>
>>On the contrary, the condition being described was that the majority
>>had a strong preference. Under Range, all they need to do is vote
>>that preference as a strong one. What coordination does this take?
>>
>Again "strong preference" for what exactly?  And how strong is "strong"?

The strongest preference is expressed in range by rating the 
undesired outcome at the minimum rating and the desired outcome at 
the maximum rating. If the majority does this, and if they are in 
agreement about these two things, they will prevail.

"Strong preference" means strong preference for a desired outcome. If 
they only have a weak preference, and express such a preference, they 
might not get it.


>I  suppose it would be too much to expect any examples or evidence 
>in support of this
>fantastic nonsense?

That is correct. I don't waste my time providing evidence to support 
fantastic nonsense. At least not usually.

>Range has no real "majority-rule" related guarantees, except a very 
>unimpressive weakened
>version of  Minimal Defense that means that for a majority to block 
>the election of X they
>must both give X a minimum rating and some other candidate a maximum rating.

Yes. In other words, they express a strong preference.

>But since Range is a deterministic method, the lack of guarantees 
>for the majority necessarily
>make it vulnerable to strategy.

There are value judgements embodied in the language used that 
essentially incorporate the conclusion. "Strategy" is a code word for 
voting insincerely in order to gain some desired outcome. Would one 
do this for a weak preference? Would you steal for a penny? Again, 
this is consistent with the world view that Chris expressed above. He 
expects that people would engage in a conspiracy to vote insincerely 
in order to impose their weak preference on the society.

No, if they are actually going to do this, they have a strong 
preference. Their so-called "strategic vote" is actually a sincere one.

Let's look at what Chris comes up with:

>25001: A99>B98>C0
>25000: B99>A98>C0
>49999: C99>A0=B0

Right off I'll note that these votes are preposterous. People will 
not vote, in such numbers, anything like this. (Indeed, this is a 
difficulty in studying Range. The votes are *complex*. This is one 
reason why we really need trials of Range.)

What we have here, if we accept this preposterous vote (which is 
carefully designed to be hair-edge, with society divided exactly into 
two diametrically opposed factions, the supporters of A and B being 
one faction, the difference between A and B being minute, and the 
supporters of C. The factions are essentially identical. No election 
method is going to produce a satisfactory result in this situation. 
It is entirely unclear to me which of the three candidates is 
actually the best. We know that A and B are essentially identical in 
support. (99 to 98 is as weak a preference as one could express in 
the system being used). And the support for C is almost exactly identical.

If B were to drop out and this election were to be held over, we 
might think that A would win, 50001 to 49999. But, wait a minute. 
These margin, a 2 vote edge, is well within the margin of error known 
to be associated with counting ballots in real elections. And the 
voters would change.

Bottom line, though: if I could make a suggestion to this society, it 
would be that you need to find a candidate with broader support. Any 
winner for this election, among the three presented, will result in a 
badly fractured society, an officer who is *detested* by half the people.

>Here a majority express the strongest possible preference that C not 
>win without falsifying their
>sincere rankings, and yet C wins.  This demonstrates (proves) that 
>Range fails Majority Loser,
>Condorcet, Majority for Solid Coalitions and (regular) Minimal Defense.

Yes. It does not satisfy those criteria (though I haven't examined 
all of them in detail, I presume that Chris is correct; certainly we 
know that Range is not a Condorcet method. All of those criteria 
neglect preference strength, and the point we have been making, over 
and over again in these threads, is that criteria that neglect 
preference strength are intrinsically inferior for evaluating the 
social benefit of an election method.

Range, of course, fully considers preference strength, with only one 
assumption: the strongest preference of each voter is equated to the 
strongest preference of every other voter. Unless voters, for some 
reason, don't vote the extremes. It's possible, some people will do it.

So what Chris comes back with is a tautology: but Range does not 
satisfy these non-preference-strength criteria. Yes, it does not. 
That was the whole point!

>These failures make Range in this case vulnerable to Compromise 
>strategy. If  the 2500 B99>
>A98 voters change to B99=A99, the winner changes from C to A (who 
>they vastly prefer).

Well, I would have to assume that the serious closeness of this 
election would be known. A shift from 98 to 99 is hardly a major 
shift. I've recommended that Range elections include a facility for 
expressing Favorite *without* giving a higher rating. I've also 
recommended that Range be coarser, not 0 to 99, I'd rather see 0 to 10.

Now, note that I proposed, in these and concurrent threads, a safety 
feature, a runoff if the preference winner were different from the 
Range winner. I did not specify what kind of preference winner, but 
let's assume that it would satisfy Condorcet. This election would 
have A as the Condorcet winner and C as the Range winner. (Both by a hair.)

If votes did not change (unlikely in itself), A would prevail, I 
presume. In the context described, where compromise is very unlikely, 
C would fail a ratification vote, and C would also fail in a top-two 
runoff between the Range winner and the Condorcet winner.


>25001: A99>B98>C0
>25000: B99=A99>C0  (sincere is B>A>>C)
>49999: C99>A0=B0
>
>This Abd, is *proof* that Range is vulnerable to the 
>Compromise(compression) strategy.

I don't consider that a vulnerability. Vulnerability implies that 
there is something wrong with it. Remember, the "sincere" vote here 
was A99>B98. That is essentially equality. We don't hold preferences 
with that kind of precision. (That's one reason why I argue for 
coarser Range, with Favorite designation)

What Chris continues to do is to use the language of preference. 
"Sincere is B>A>>C." He incorporates here a slight increase in 
expression of preference strength (">>"). But what I'm noting is that 
the B voters, we can call them, are so close in their estimation of A 
and B that the difference is well within the noise.

This example does not show any kind of objectionable strategic 
voting. If they don't vote "strategically," we can say that the 
"majority" gets C, which they detest. But, realistically, half the 
society is going to get a leader they detest.

Chris, it seems, is unconcerned about this. He'd be content for A to 
win, too bad about the C voters, they were two votes short of winning 
the whole show.

As I've said before, the *real* problem is single-winner for 
representative elections, and long terms for officer elections. In 
the scenario described, some kind of power sharing between A and/or B 
and C would make sense. But what a divided society! I think it needs 
much more than an improved election method!

This is more interesting:

>36: A99>B98>C0
>18: B99>B98>C0
>46: C99>A0=B0
>
>This time the AB have a comfortable enough majority to win without 
>insincere equal-ranking, and
>A (the Condorcet and IRV winner) wins.  But Range (like Approval) is 
>vulnerable to a form of
>Burial with a nasty defection incentive.
>
>36: A99>B98>C0
>18: B99>B0=C0   (sincere is B>A>>C)
>46: C99>A0=B0
>
>The 18 B voters have "defected" from the AB coalition by insincerely 
>changing from B99>A98
>to B99>B0=C0, and Range rewards their dishonesty (and disloyalty) by 
>electing B.

Now, why would they do this? Only if they strongly prefer B to A. But 
this contradicts the initial conditions.

What Chris is really doing is presenting us with a scenario that 
contradicts the assumptions made in constructing it. In the example 
given, the "sincere" votes, the A voters *slightly* prefer A to B and 
the B voters *slightly* prefer B to A. *Very* slightly. And yet we 
imagine that the B voters are going to lie about their preference, in 
cahoots with each other, in order to elect B? Why? *They don't really 
care whether A or B is elected.*

And the A voters, even if the B voters do this, what do they think?

*They won't care!* Supposedly this is some kind of bad outcome, but 
it satisfies the majority of voters, 54%, *quite* well. We've seen a 
lot of elections that did not do so well....

(However, there is one possible outcome of this. The A voters, seeing 
the poll results, may suspect that they were wrong in thinking that A 
and B were about equal. If the only real difference between A and B 
is that they represent different parties, and what we are seeing here 
is *party* behavior, the A voters may well decide that there is 
something drastically wrong with the B party, and they will never 
again give any decent rating to a B party candidate. B might win the 
election and the B party might disappear as an effective political 
force. Betrayal is not a way to win friends and influence people.)

>>Majority Rule. What a concept!
>Yes. Please make up your mind whether you are in favour of it or not.

I have explicitly stated, numerous times, that the Majority have the 
right of decision. Methods, however, that neglect preference strength 
deprive the Majority of necessary sophistication in making that decision.

What I really prefer is majority rule through full deliberative 
process. Election process typically is *not* deliberative, it is 
purely aggregative, in that the kind of give and take that is an 
essential part of deliberative process, with procedures for amendment 
and so forth, is missing. Asset Voting is a specific remedy for this.

Note that Chris, in eliminating the context for this quote, actually 
cut out the procedure being recommended that would provide 
decision-making power to the majority, in a more sophisticated manner 
than, say following the Majority Criterion.

The Majority Criterion properly applies (i.e., is desirable) to 
binary elections. It gets dicey when there are more than two choices.

About the ratification or runoff proposals I made:

>"Majority winner" (presumably referring to a single candidate who is 
>the favourite of more than
>half the voters) and "Plurality winner" both have a split-vote 
>problem (failing Clone-Winner) and
>of course there isn't always a Condorcet of "Majority" winner.

In the context, the meaningful winner that makes it worth examining 
the election more closely with a ratification or runoff would be the 
Majority winner. Yes, there is not always such, just as there may not 
always be a Condorcet winner, but that was the point. If there is no 
Majority winner, then there is no reason to consider that the 
election of the Range winner is in some way violating the majority principle.

The idea of a ratification was to ensure that the winner was 
*accepted* by at least a majority of the voters. In that 
ratification, "accepted" may take on different tones than were 
expressed in the election itself.

>>(I oppose public campaign financing, it is the wrong approach, but it
>>*does* exist and is going to be a problem in election reform.)
>>
>It works quite ok in Australia. What do you suggest to address the 
>unfair advantage of  Big Money
>in election campaigns?

The problem is not Big Money, for Big Money is actually pocket change 
for the 800 lb. gorilla who is, unfortunately, sound asleep.

The problem is that the electorate itself is not organized except 
through the defective mechanisms of electoral democracy.

A U.S. Presidential election runs perhaps a few hundred million 
dollars per candidate (this is just a figure that comes to mind, I 
don't think it is radically wrong). That's less than two dollars per citizen.

Now, if the citizens don't care enough to directly fund elections, 
something is drastically wrong, and it is not Big Money.

Chris, I think, knows that I have a very specific answer for this. 
The problem is that the electorate is not organized directly, and the 
solution is an organizational technology that would make it practical 
to do this. It requires, indeed, thinking outside the box.

For some strange reason, professors of political science write books 
about democracy that completely neglect the institution of the proxy, 
which enables representative democracy *without* elections. It is 
generally considered that direct democracy is ideal in small groups, 
but, of course, that it is impossible on a large scale. But the 
possible impact of the use of proxies has never been considered by 
the political science establishment, and delegable proxy, which 
theoretically should make direct democracy practical on a very large 
scale (larger than earth population), is, of course, entirely unknown to them.

Proxy democracy has existed for hundreds of years, and is in nearly 
universal use in business, for the governance of corporations. But it 
is never considered for political use.

Why? A paranoid view would be that the powers that be realize that 
this would actually give power to the people. However, I don't think 
that they even realize this. I don't think the idea has occurred to them.

Proxies are used in corporate governance because the shareholders 
insisted on it. They did not want to have to personally attend 
meetings, and holding elections for representatives made no sense at 
all, why couldn't they just send a proxy?

Again, what is different about a corporation with all shareholders 
owning one share, and a society with members each having one vote?

I can tell you: the first is voluntary, you can leave, sell your 
shares, and the corporation does not exercise sovereignty over you, 
rather it serves you. Leaving a country is ... more difficult. 
Sometimes it isn't even possible.

However, the vision of the government as a servant of the people is 
one that has been advancing over the last couple of centuries.