[EM] Lomax SFC & RV reply

[Michael Ossipoff]

Lomax said:

Just to be explicit about the application of this to equal ranking. At 10:28 
AM 2/15/2007, Chris Benham wrote: >Pasting from Mike's page: >> >>Some 
definitions useful in subsequent criteria definitions: >> >>A voter votes X 
over Y if he votes in a way such that if we count >>only his ballot, with 
all the candidates but X & Y deleted from it, >>X wins. [end of definition]

Lomax comments on that definition:

Equal ranking of X and Y is clearly not voting X over Y.

I reply now:

No one will disagree with you there, Mr. Lomax.

Lomax continues:

If we modify the ballot as stated and this is the only voter, it's a tie.

I reply now:

How so? We look only at one ballot, with all candidates but X and Y deleted 
from it.

If, in SSD, that voter has ranked X>Y, that most decidedly is not a tie. X 
wins as CW.

If, in Plurality or Approval, the voter has voted for X and not for Y, that 
most decidedly is not a tie. X wins.

Referring to the below, I hope that, at the website, I made it clear that 
when I say “preference” in those definitions, I mean “pair-wise preference”. 
If I haven’t, then I must.

Lomax quotes my definitions:

>>Voting a preference for X over Y means voting X over Y. If a voter 
>> >>prefers X to Y, and votes X over Y, then he's voting a sincere 
>> >>preference. If he prefers X to Y and votes Y over X, he's >>falsifying 
>>a preference.

I don’t recognize the following as my definition of equal-voting, but it’s 
probably acceptable as a definition:

Equal voting is neither voting a preference nor falsifying a preference. It 
is not expressing a preference.

I don’t know if Lomax wrote that, or whether he quoted it from the website. 
I usually use a different, more explicit, definition of voting X equal to Y.

Lomax continues to quote my definitions:

>>A voter votes sincerely if he doesn't falsify a preference, and >>doesn't 
>>fail to vote a sincere preference that the balloting rules >>in use would 
>>have allowed him to vote in addition to the >>preferences that he actually 
>>did vote.

Lomax says:

I find the application unclear. What is undefined is what it means for an 
election method to "allow" the expression of a preference.

I reply now:

For one thing, the definition refers to what the balloting system in use 
allows, not what the method’s other rules allow.  In Plurality balloting, 
for instance, that balloting system doesn’t allow you to vote more than one 
candidate over anyone. In Approval, the balloting system allows you to vote 
all of one set over all of the remaining candidates, but it doesn’t allow 
you to vote preferences within those two sets.

Nothing is undefined in my wording (unless I forgot to say that “preference“ 
means “pair-wise preference“. Say, in Plurality, you vote for Nader. You’re 
voting Nader over everyone. To add a voted preference for Clinton over 
McCain, you’d have to give up your voted preference for Nader over everyone. 
So when you fail to vote a preference for Clinton over McCain, in Plurality, 
you are not failing to vote a preference that the balloting system in use 
would have allowed you to vote in addition to the preferences that you’ve 
actually voted.

Lomax continues:

Plurality allows the expression of a preference. Unfortunately, it only 
allows the express of a preference for one candidate over all others.

I reply now:

Yes, but I don’t call that one preference. I call it pair-wise preferences 
for that one candidate over each one of the other candidates. You’re voting 
a set of pair-preferences when you cast your Plurality vote.

Lomax continues:

Approval allows the expression of a preference for a set of candidates over 
all others. If the ballot allows complete ranking and allows equal ranking, 
then any use of equal ranking where a preference actually exists, no matter 
how small, would be considered a failure to "vote sincerely."

I reply now:

So far, so good.

Lomax continues:

While one can define terms any way one likes, it would seem inadvisable to 
define them in a way which flies in the face of ordinary usage.

I reply now:

Mr. Lomax, you neglected to tell me how my definition flies in the face of 
ordinary usage.

Well, ok, I have said on EM that “sincere and complete” should, ideally, be 
substituted for “sincere”, as the name for the kind of voting that I define.

I’ve also considered calling it “free voting”, because the voter freely 
votes all the preferences that the voter is allowed to vote on the same 
ballot (that’s a very loose wording).

The point is that, when someone votes as described in that definition, s/he 
is voting his/her preferences exactly as s/he feels, without falsifying or 
holding-back in the way that strategy could force someone to do.

But you’re right, that another word would probably be better, to clarify 
that I’m not accusing that voter of dishonesty if s/he doesn’t vote in that 
way. It’s intended only as a description of voting that isn’t hampered by 
strategy needs.

I hope I’ve clarified what I mean by that definition. I should probably 
substitute “Sincere and complete” or “Free” for “sincere”.

Lomax continues:

But what if a ballot does not allow complete ranking, or does not have 
enough rating levels to accomodate all candidates?

I reply now:

In that case, failure to vote all of one’s pair-wise preferences wouldn’t 
violate my definition of sincere voting. We’re all making the tacit 
assumption that, with ranking methods, the ballot allows as many rank 
positions as there are candidates.

Lomax continues:

It appears that the interpretation being used is that these methods don't 
satisfy SFC, but this would be because they don't satisfy the criterion even 
without "falsification."

I reply:

RV would fail SFC no matter how many rating levels it allows. Yes, Condorcet 
wv would fail SFC if it didn’t allow as many rank positions as there are 
candidates.  As I said, the tacit assumption is that it allows at least that 
many rank positions. In an actual election, if the ballot doesn’t allow as 
many rank positions as there are candidates, one could say that the wv 
Condorcet implementation in use there fails SFC. But the method _itself_ 
doesn’t fail SFC, because, with sufficiently many rank positions it passes. 
And, when judging method compliance, we assume that there are enough rank 
positions available.

Lomax continues the quote:

>> >>SFC: >> >> >> >> >>If no one falsifies a preference, and there's a CW, 
>>and a majority >>of all the voters prefer the CW to candidate Y, and vote 
>>sincerely, >>then Y shouldn't win. >> >>[end of definition] Now, this has 
>>been about the definition of the criterion. Even if equal ranking in the 
>>presence of a sincere preference is not falsification, Approval, for 
>>example, fails SFC.

I reply now:

Correct.

Lomax continues:

Yet, I've argued, it fails SFC because it does better.

Come again? <smiley>

Lomax continues:

It is clearer with Range: If no one falsifies a preference in Range of 
sufficiently high resolution, and all preferences are expressed, that is, 
equal rating is only used for absolute equality of rating, then Range still 
fails SFC

I reply now:

Correct again. RV fails SFC. And not just on a technicality. RV doesn’t give 
the freedom from strategy-need that SFC-complying methods give.


Lomax continues:

, and it is easy to construct scenarios where it does so by choosing a 
winner who is clearly "better" for society and for the members of society 
individually, than the Condorcet winner.

I reply now:

Lomax, we’ve been all over this: Yes, if society consisted only of people 
whose only goal in the election was to sincerely express their ratings, in 
order to do their part to maximize SU, then RV would be great. But the real 
world is not like that.

Lomax continues:

This is because of preference strength. If the CW is preferred, by a 
majority to a candidate A by a majority with a very small preference, such 
that, for practical purposes, these voters will be equally happy with the 
election of the CW or A, and a minority of voters strongly prefer A, such 
that they will be happy with A and seriously unhappy with the CW, it is 
quite clear that A should win.

I reply:

No, it is not. Yes, it would be better for SU, if people vote sincerely and 
maximize SU in RV. But when you kiss-off majority rule, you also kiss-off 
freedom from RV’s avoidable strategy dilemmas. We don’t have an 
SU-maximizing electorate, so let’s at least do what we can to give voters 
freedom to vote their preferences without need to strategize.

Lomax continues:

A makes *everyone* happy, the CW in this situation only makes a bare 
majority happy. Thus, we conclude, the Condorcet Criterion *must* be 
violated in some elections by an optimal method, and thus this theoretical 
optimum method must fail the criterion and others similar to it, such as the 
Majority Criterion and SFC.

I reply:

…optimal in a Utopia where voters aren’t interested in benefiting 
themselves, but are only interested in doing their part of maximize SU, only 
interested in the overall greater good.

Lomax continues:


Of course, we need a definition of "optimal." I've been suggesting that it 
should be explicit. Too often, when we consider methods by election 
criteria, we assume that a criterion is desirable, entirely apart from 
whether or not it chooses the optimum winner.

I reply:

Wrong. You don’t get an “optimal winner” in any sense if voters are forced 
to do other than vote their genuine preferences. By trying to offer more 
freedom, RV only stifles freedom to vote sincerely.

Lomax continues:

It's *assumed*, very easily, that the majority choice is the optimum winner 
-- and therefore it is desirable to satisfy the Majority Criterion -- when 
this is certainly not clear enough to be reasonably an axiom. Any person or 
business which makes decisions failing to consider the strength of 
preferences will soon run into trouble.... Perhaps I should be more explicit 
about this. In considering a decision among many choices, I may consider the 
effect of each choice on various aspects of my life. With each aspect, I may 
have a preference among the choices. If we model the importance of an aspect 
by a number of voters voting according to that, then systems which only rank 
but do not consider preference strength can seriously fail to make an 
optimum decision. The additional necessary element is to incorporate 
preference strength.

I reply now:

Lomax is still working within the framework of a Utoptian society with an 
electorate bearing no resemblance to ours.

Lomax continues:

Decision-making strategies often use this, quite explicitly. One will give 
weight to various aspects of a decision, and for each aspect a numerical 
rating can be used. Then, for each choice, the rating is multiplied by the 
weight and the product noted for each choice. The choice with the highest 
total is considered the best.

I reply now:

Of course that’s a good decision making method, if you have the information 
that it needs. Sometimes you might not have a good estimate of the actual 
ratings, but might know how you’d rank them, with respect to each 
consideration. Then use Borda. Each considerations is a “voter”. Rank the 
alternatives’ merit with respect to each consideration to get a set of Borda 
ballots (if you don’t have the ratings estimates need for an RV count).



Lomax continues:

Warren points out that Range Voting is used by bees.


I  reply now:

Did Warren ever justify that statement?


Yes, for your own decision making, it’s safe to assume that you’re not going 
to strategize with your RV ratings.

Mike Ossipoff