[Election-Methods] Response to Schudy re Range vs Approval voting

[Abd ul-Rahman Lomax]

At 04:09 PM 8/9/2007, Juho wrote:
>In this discussion I'm quite sensitive to different wordings that are
>used when describing Range.
>
>[...]
>
>I used term "sincere" roughly to refer to voters marking their
>personal candidate utility values in the ballots. Or if you don't
>like the word "utility" then we can just talk about putting
>candidates on the value axis without putting any special emphasis on
>the min and max values.

"Roughly." What is a "personal candidate utility value"? What Juho 
did was to simply use a different set of words, without describing 
the *meaning*, i.e., how the voter is to arrive at this set of values.

How do I put the candidate values "on the value axis"?

What determines what I call the "magnification"?

Suppose that I try to estimate candidate values by the following 
procedure: I consider the payment that I would want to personally 
receive in order to allow the election of a candidate, or pay in 
order to guarantee that election. This would establish what are 
reasonably called "absolute utilities." It doesn't matter if I'm rich 
or poor, we would only need to consider that if we are trying to make 
my utilities commensurable with those of others.

Now, I have absolute utilities. They measure and compare the value of 
the candidates to me. If I wouldn't pay a nickel to elect so-and-so 
over his opponent, I must not have much of a preference. Unless I 
don't have a dime to my name. In which case I'd simply measure the 
utilities in terms of how many minutes I'd spend for the cause, or 
any other measure.

Now, I am faced with a specific election, Range 100. Do I consider 
who is actually *in* the election when I vote? From what Juho has 
written, I'd have to assume that to be "sincere," I would not. So; 
none of the present candidates are anywhere as near as good as the 
Messiah, and none of them are anywhere as bad as the Antichrist. For 
the Messiah, I'd spend everything I have and might even borrow, for 
the Antichrist you couldn't offer me enough. Let's see, maybe I could 
scrape together a couple of hundred thousand dollars, pulling out all 
the stops. So we have at one end, the Messiah, $200,000. At the 
other, negative infinity! (Yes, this is correct. I wouldn't do it for 
the world.) For the election of Al Gore, in 2000, I'd have paid 
easily $1000, if I knew it would have been effective. Possibly more. 
(The rules have to be that nobody will help me....) (I would now pay 
more.) To accept the election of Bush, $5000 might have been enough. 
(It would be a *lot* more expensive now that we know the man better.) 
Let's see.

If we use an absolute scale, linear, everything ends up at negative 
infinity. However, there is another procedure. I could decide to fix 
the midpoint at 50%. Then I scale positive utilities in the range of 
50% to 100%, and I proceed down an equal amount. This, then, 
truncates at -$200,000. Anything that low or lower is zero.

So what do I come up with as so-called "sincere" non-normalized Range 
Votes? Range 100, 50.25% for Gore. Bush is below 50% by five times as 
much as Gore is above it, so Bush is 48.75%. Rounding off for Range 
100, it is Gore 50%, Bush 49%. My sincere votes.

If this is not what "sincere" vote means, please explain what is!

*Everybody will normalize, at least to some degree!* And many will 
"truncate," which means that they place the ends of the Range Voting 
scale on their absolute scale *within* the candidate set such that 
more than one candidate is at an end point.

And there is nothing "insincere" about this. If I give a candidate 
more than zero, I am contributing something to the possible election 
of that candidate. It is easily possible that I would not care to do 
that for more than one candidate. Or am I *forced* to make a choice, 
to assign a higher utility to Adolf Hitler than to Genghis Khan -- or 
the reverse?

Let me repeat this: there is no clear definition of a "sincere" vote 
in Range. Indeed, the whole concept is suspect. If the Republican 
supporters of R2 in the example given by Juho previously did not have 
a strong preference for R2 over R1, why did they vote max strength 
for R2 over R1? Juho, following others, will give the reason as "they 
wanted their favorite to win." But *how much* did they want their 
favorite to win. If this is the most important thing to them, they 
voted sincerely!

Their vote, as an action, abstained from the election between D and 
R1. It is as if they were saying, "R2 or I don't care." And if that 
is how they feel, who are we to called it "strategic"?

What Juho and others do is to posit a weak preference that is 
expressed as a strong one, but ignored is the *motivation.* I have 
*never* seen a critic of Range present the reason why they might do 
this, it is passed off as "they wanted to win."

Okay, they wanted to win, that is, they wanted R2 to win. How badly? 
One full vote. So that is what they cast.

What's the problem? They expressed what they wanted, and how much 
they wanted it. If you lie about this, you might get what you ask 
for. By abstaining from the D/R1 election, these voters have informed 
the system that they don't care about it. So it will not consider 
them *at all* in that pairwise election. And if that turns out to be 
the relevant one ... they get a much worse outcome than if they had 
voted "sincerely," which in this case means with the supposed "real" 
preference that they have. They *actually*, it is posited, would 
greatly prefer R1 to D.

But all this is concealed under the hood, the critic just posits the 
contradiction, knowing -- or he should know by now -- that most will 
not notice that two opposites are being presumed.

>The voters could be harmed considerably in some cases. There have
>been several examples.

None so far that show "considerable" harm. Indeed, none that show 
harm at all, only less benefit, possibly.

>  One could e.g. translate utility values 1
>A=90, B=80 and 1 B=90, A=70 to actual votes 1 A=100, B=0 and 1 B=90,
>A=70.

You can translate them how you choose, as can the voter. But you are 
assuming utilities that have already been translated, and you are 
translating them again, arbitrarily, but making assumptions about 
what they mean.

Juho has never addressed what absolute utilities might be, but he 
seems to assume that they exist. Yet absolute utilities as shown are 
percentages of what? Are they dollars? What are they?

Generally, we look at relative preference, but there is nothing to 
tie these preferences to the endpoints of the scale. I have no idea 
if the translations Juho mentions above are reasonable or not, no 
clue. The translated votes could be normalized and fully sincere.

There may be other candidates present who affect the translated 
utilities, plus the voter may be considering election probabilities. 
Consider this election. Shall we:

(1) Build a new public safety complex.
(2) Continue with the old one.
(3) End all local taxation and refund the entire accumulated taxes to 
the citizens, proportionally to taxes paid.

Range Voting. Now, #3, under some conditions, sounds nice. If I want 
a public safety complex, I could donate to it. However, I happen to 
know that option 3 got on the ballot by a fluke, and it hasn't a 
prayer of passing. So should I consider it in determining how I vote? 
If I think (3) desirable, should I downrate my favorite of the others 
to be "sincere."?

I'd say not. I'd say that in any election where there are only two 
reasonably possible outcomes, the sincere vote, normally, *in 
competitive public elections*, is to pick one and vote fully for it. 
Only if you really don't care would you vote something else. In which 
case *you don't care*, so you will hardly be harmed no matter what 
the outcome is. If I want 3, fine, I can vote 100% for it. And 100% 
for my favorite of the *real* options, and zero percent for the other.

There is nothing "insincere" about this. And, indeed, this is how 
most people presently vote, and I see no reason for them *at all* to 
discontinue it. Range Voting gives them some more options, most 
notably it gives these options to two classes of people: those who 
prefer a third party candidate, and those who prefer one of the major 
party candidates, but would like to show some support for a third party.

(The latter might be because they want to influence their own party 
to move in that direction.)

>The effect on the society could be e.g. bad election results (e.g.
>worse candidate A elected due to strategic voting) or Range becoming
>Approval in practice.

First of all, the possibility of "bad election results" has been 
brought up again and again, in the face of requests to show a "bad" 
example, and none has been forthcoming, so far. That A is "worse" is 
*assumed,* not shown. In the example given, the candidate elected 
isn't clearly worse, and that candidate was only elected because the 
majority actually gave the candidate a high rating. They like him! So 
how is this a "bad result"?

>I think we have covered all this before. Let's try to avoid repeating
>the cycle.
>
> > "Insincere" refers to reversing a preference;
>
>That's one option. In natural language I'd include also other cases.

Failing to give the last intimate detail of preference? Like I'd 
probably prefer cyanide to being torn from limb to limb? Do I get to 
vote zero for those two without being "insincere"?

Juho has consistently failed to address the issue. He has not defined 
what a sincere vote is, beyond saying that it is some kind of 
expression of "personal utility," which simply begs the question. 
What is a "personal utility" and what does it have to do with Range 
Voting? Range Voting is a *voting method*, whereby the votes of 
voters are aggregated to produce a result. It happens to be that if 
voters vote what might be called "relative expected satisfaction," 
generally, Range Voting maximizes it. But there is no clear standard 
for what the actual numbers would be.

If somehow voters can vote *absolute* utilities, and they actually do 
it, Range would truly choose the overall best candidate. But this is 
extremely difficult to arrange, and it really has nothing to do with 
the question before us, which is the effect of so-called "strategic 
voting" in Range.

By refusing to confront the basic issues -- what is a "sincere" Range 
vote -- Juho is simply stirring the pot, over and over, without 
adding anything to the soup. He keeps asserting that "strategic" 
voting harms the "sincere" voters, but he hasn't defined sincere in 
any clear way, nor strategic, nor shown harm.

>(sincere votes)
> >>  You seem to be recommending the voters to primarily do so,
> >
> > I do recommend not reversing preferences. As to the expression of
> > so-called sincere ratings -- what is that?
>
>Defined above. (I didn't refer to reversals specifically.)

It was not defined above. A putative synonym was given. I gave some 
hints as to how it might be done, but it is far more complex than 
Juho seems to imagine. Suppose I've decided that to be "sincere" is 
cool. I want to vote "sincerely." So how do I do it. How do I decide, 
exactly, what my "sincere votes" would be. I gave an example using 
absolute utilities. It resulted in me voting 50 for Gore and 49 for 
Bush. There is something obviously wrong with this. But what would 
Juho propose in its place?

Everyone writing on Range, who understands the method, recommends 
that voters normalize to the real election set, *unless* conditions 
are such that some broader scale be used, in which case you would see 
votes like Juho posits. But those conditions are that there is some 
agreed-upon measure, some way of making utilities commensurable, so 
people know what 100% is and 0% is.

In the pizza election, the common understanding is that 100% means 
"this is my absolute favorite variety ever." and 0% means "I can't 
eat it." So in that context, sincere people know how to vote, and 
they may very well not vote the extremes in a particular situation, 
looking at the menu. Those pizzas may not be on the menu, so they 
would not vote the full range.

But what is the standard for public elections? Establish one, we can 
talk about not normalizing! Until then, very, very few people will 
not normalize. So, please, forget about these examples where 50% of 
the voters are Democrats, and they vote 80% for one Republican and 
70% for the other Republican! I showed how they would vote, in reality....

>It seems you recommend not to normalize the estimated frontrunners to
>min and max.

This did not follow from what I wrote. With pure Range, and no public 
ballot imaging, I'd recommend normalizing the frontrunners, period. 
Vote the rest how you like, it doesn't matter! But if you were wrong 
in your estimation of who the frontrunners are, you are less likely 
to regret the vote if you vote intermediate votes if they are appropriate.

Mean-based Approval is quite a reasonable strategy. In practice, it 
tends to average out over many voters. However, the presence of even 
a few voters who vote intermediate votes, it appears, improves the 
outcome *for the Approval Voters and the "Sincere" Voters.*

I've been saying this over and over, Juho hasn't, so far, 
acknowledged it. I'm not sure that he understands it. The claim is 
based on actual calculation in a large Range 2 election, by comparing 
the relative expected outcome for optimal votes in the Range 
election, and then the relative expected outcome if *all* votes are 
limited to Approval style.

With the assumption that the single intermediate vote available in a 
Range 2 election (0,1,2) is an accurate expression of voter 
preferences, the expected utility for the "sincere" voter is 1.40. 
This is a relative utility, not an absolute one; it assumes that the 
voter's vote can affect the outcome. All other initial conditions 
(the votes without this voter) obviously leave the voter's vote moot, 
so they cannot affect expected outcome. If the voter votes Approval 
style, in large elections, the vote of 200 and 220 have the same 
expected utility, also 1.40. However, if we remove the possibility 
that *anyone* votes an intermediate vote, the expected utility is 
1.33. By eliminating the possibility that others could cast 
intermediate votes, we have lowered the expectation for the *Approval 
Voter* and we have lowered it for *every* voter, since now all voters 
must vote Approval style.

Do the math! I find it quite interesting!

> >>  With this I think we are back in the
> >> original claim that Range may create a mess if some voters vote
> >> sincerely (and maybe are guided to do so) and some strategically.
> >
> > No such mess has been alleged specifically. Rather, Juho and others
> > continue to claim that a mess is created, but not *specific*
> > scenario that deserves the name is mentioned.
>
>There have been examples. See e.g. the example I gave above.

No example of "mess" has been given. What Juho does is to posit some 
votes and assert that the outcome is a "mess" or a bad outcome, but 
the votes don't show that. Nor have any reasonable conditions 
underlying the votes show that.

I'll note that if a majority of voters vote stupidly, you can 
certainly get bad outcomes! So it is remarkable that Juho has not yet 
asserted anything like what he claims!

> > It balances out. And I expect the same with elections.
>
>Do you mean in the first election the strategists might win but in
>the second election most voters would vote in Approval style?

No. I mean that if everyone votes sincerely, in one election it might 
seem that I lose something, but it will be small, and in return 
someone else gains something more than I lost. Next election, I'm the 
one who gains more than someone else gave up.

Elections are not a zero-sum game. If they were, the situation would 
be quite different. In the elections that Juho posited, everyone 
gained something, most likely, no matter which candidate won. But 
Juho asserted that it would be a "mess" if one of the candidates won.

What appears to me is that in some elections, those who vote Approval 
style may possibly gain some advantage for themselves, but at little 
cost to everyone else. If any! (Usually not!) In other elections, 
those who vote Approval style when a different vote would have been 
truer to their relative preferences may regret the vote. Overall, it 
looks like these two effects, in a way, balance each other out, but 
the Approval approach, as we might expect from the extremity of the 
vote, swings wider. The more accurate vote is less likely to help the 
voter personally, but also less likely to harm.

I'd suggest to Juho that looking at the study previously published 
here (I post very few original subjects, this was one of them), in 
detail, could reveal a lot. Read the thread, there were errors in the 
original spreadsheets, and some conclusions were reversed.

(One fascinating conclusion was that with utilities of 2, 1, 0, for 
the candidates, Range 2, the Approval vote of 220 and 200 were *not* 
balanced, the vote of 200 has substantially higher utility *in an 
election with a small number of voters.) However, in large elections, 
many voters, the difference becomes vanishingly small.

> > In Range the preference of a majority can be passed over for the
> > broader satisfaction of the whole electorate, including a minority
> > with a stronger expressed preference.
> >
> > *This is not a problem,*
>
>Coming voluntarily back from Approval style to sincere votes is not
>as bad as starting from and recommending the use of sincere votes to
>all. (But it doesn't necessarily work that way either.)

*Nobody* has "recommended the use of sincere votes to all." Who did this?

I don't even know what a "sincere vote" is, though I can define 
certain kinds of insincere ones, starting with the obvious: 
preference reversal.

Beyond that, I could define an insincere vote as one where preference 
strengths are obscured. But this isn't nearly as clear as reversal. 
*How much* obscuration is involved?

It appears that if the voter normalizes, which Range supporters 
expect for the vast majority, little harm is done by voting 
intermediate expected satisfaction "accurately," a term I prefer to 
"sincerely." If the voter normalizes to the frontrunners -- which is 
what experts recommend, generally -- there is even less harm; indeed, 
very little, if any. I've never seen one of these supposedly bad 
outcomes where normalization to the frontrunners was done. Indeed, 
the issue isn't even considered, and the examples which we have seen 
don't show normalization *at all*.

Range Voting, some argue, is not Independent of Irrelevant 
Alternatives. But that actually depends on the voter's strategy. With 
some strategies, it is independent.... The method itself is 
independent. Only if the voter changes votes does it become 
dependent.... What happens is that if a voter downrates a formerly 
max rated candidate because a better one appears, the former one 
could lose to a third candidate whose supporters were not affected by 
the introduction. But if that is the environment, the voter would be 
foolish to downrate that way. Rather, a voter would better max rate both.

I've suggested that a method be introduced to indicate preference 
without changing range rating. It would be used for a number of 
purposes, including pairwise analysis for a runoff, or assigning 
campaign funding, or the like. It isn't really necessary with 
high-res Range, but it could be more important with low-res, like 
Approval (Range 1) or Range 2.