[EM] range voting, properties with strategic re-voting, and utilitarianism

[Warren Smith]

>> --Also, now that I understand DMC has two kinds of monotonicity property, I 
> must report my admiration.   

>Heitzig: Why? Many Approval/Condorcet-hybrids are monotonic in both senses.

--fine.  However, I had not seen any such methods previously,
I am ignorant.  You also mentioned your "favorite method DFC" - I
do not know what that is either...  but would like to (or in fact any other
methods you think I should know about but do not).  [Incidentally, in return,
I have invented a few methods I think you (JH) would want to know about...
namely "sinkhorn voting" and "maxtree voting".  The former is related to markov
chains.  The latter is very related to your "river" method but seems to me superior to it.]

>Benham: Range  only has  this property in a technical sense,

>A third candidate, C is nominated.
C is  a  horror far-right candidate. Maybe some of  A's supporters are 
members of some ethnic/racial/religious minority  that the C
candidate says he's in favour of  persecuting. Anyway, now all the mass 
media have to do now is to convince some of  A's supporters
that C has some chance of winning the election, or just that they should 
give a maximised sincere vote.

So without  C we have:
52: A99, B0
48: B99, A0
A wins 5148  to B4752.

With C added  and some of  A's supporters conned and/or frightened, this 
could become:
47: A99, B0, C0
05: A99, B98, C0
46: B99, A0, C0
02: C99, B98, C0

Now B wins:  B5242,  A5148,  C198.   (Approval is also vulnerable to 
this scenario.)
>(End of Benham)

--What is going on here is a subtlety that is generally (always?) not mentioned in
the available literature - DIFFERENT votes arising from different strategy in the
second election.  Certainly, in range voting, adding new candidates
can affect voter strategy, so if they now get to re-vote in a new election,
they will provide different votes.   Most property discussions however
act on the assumption we are talking about the same votes, modified to
include the new candidate or remove and old one.

I have no problem with considering voting system properties in the presence of such vote-changing
two-time-strategic voters.  In fact I think it is a good idea.  It is just important that whenever
we do so, we create a new property-name-and-definition and then study IT.
For example, instead of "PROPERTY", call it "PROPERTY[STRAT2-REVOTE]".
Thus Range Voting is cloneproof but not cloneproof[strat2-revote].
Sometimes this kind of study can be difficult since it requires understanding of strategy.

Anyhow, as I said I do not mind this kind of idea being used to criticize Range voting.
I merely ask that anyone who does so, also criticize their own favorite method
in the same way.  For example, range voting obeys the Condorcet property
under some people's (my) extended-definition of "condorcet".  (Call this property
"WDS-condorcet".) But it does not obey WDS-condorcet[strat2-revote] which happens
in this case to coincide with the other (more) common definition of Condorcet.

BUT... most "condorcet methods" touted on EM, do not obey
condorcet[strat2-revote]  or   WDS-condorcet[strat2-revote] 
either!!!!  So don't come whining to me about range voting
and pushing condorcet methods, if this is your criticism.  You have no right!

In particular, since this thread came from a discussion of the DMC condorcet-approval hybrid
voting method,  I point out that I do not believe DMC is   cloneproof[strat2-revote]  either!


> > 1. Can you explain to me the difference
> >between assigning 64 or 65 points to the middle candidate?
> > 2...there is no such thing as Util(A) or Util(B).
> 
> --1. Why should anybody have to explain it?  Why should you have
> to understand it?  Why should anybody have to feel they understand it?

>Heitzig: Well, if you don't think voters should understand the system, then I can't help it.

--They understand the system fine.   Range voting is very easy to understand, easier than 
DMC in fact.  What they do not understand, is utility values!

But DMC and all other systems also have that same problem - voters have
trouble understanding utility values and hence have trouble choosing either their most honest,
or most strategic vote.   In fact in DMC (or more simply, approval voting)
to choose your most strategic vote, you have to know the utility values
of the candidates.  If you merely know the ordering of those values, that is insufficient
information to choose the most-strategic approval-vote!

So in fact, you are trying to pretend this problem is absent in DMC, but you are wrong.
It is present everywhere.  As a first step toward progress you need to admit the true
state of affairs - which is utilitarian and that cannot be escaped, sorry - and 
then go on from there.

>>...which is only one of several possible perspectives to look from...
>> or brain chemicals, or neuron events.  
>Aha.
>> But what we definitely 
>> know is a false claim is that there "is no such thing."

>Do we know that? 
>Interesting. I don't know it since as you know I state the contrary. 

--yes we know it.  If I define a quantity, or merely show it can be defined, then
we know a definition exists.

>And if you know it, you should be able to tell me your Util(Bush) and explain it to me, right?

--wrong.  Just because a quantity exists does not mean I can explain it to you.
For example, I think we both agree that a first counterample to the Riemann hypothesis exists
(where if the RH is true then the "first counterexample" is "infinity").
But in spite of this agreement it exists, I think you cannot tell me its
value.  (If you can, please do...)  

--[Or am I dealing with that rare almost extinct breed -  a Brouwer-style
"intuitionist/constructivist" - here??! 
(who would deny even the Riemann example I just gave) Yikes...]

>> 4. My view: There is no question that utility exists, 
>> and there is no question
>> that we want to maximize it.   

>How nicely plain your world is. Ever heard of risk avoiding? Why do you think 
>people have insurances? Do you really want to claim everyone aims at
>maximizing expected (since it's never for sure) utility?

--We are revisiting an old debate (my side is called the "Bayesians" and it is generally 
agreed in the statistical community that my side long-ago won).
Anyhow.  The answer to the insurance question is that the only reason insurance is
a good idea, is that utilities of the same event differ for different people.

For example.  Suppose you are in a car crash and turn into
a paraplegic. That is an event of huge utility (but low probability) to you.    In fact it
might cost you $1 million, which you do not have.
However, from the insurance company's point of view this is an event of small
expected utility.   The point is, to a poor person, $1000 has larger
utility than $1000 has to a rich person (or insurance company).
If you are rich and already have many $millions, then you are foolish to insure
yourself against car-crash-paralysis.  Your thinking now is the same as
the insurance company's.

Hmm.  I am not saying this very well.  But the point is, the whole reason
insurance exists is that utilities differ among different people, causing
expected utilities to differ.  In fact this is the
whole reason for every economic transaction.  This is not at all incompatible with the
Bayesian utilitarian viewpoint.

To be concrete.  If an event A has probability 0.001 and money value -1000000
and hence utility -9999999999999999999999 for you since you are poor,
but probability 0.001 and utility -1000000 for me since I am a rich insurance company,
then you are willing to pay me $100 per month if I agree to give you $1000000
when A happens.  Both of us regard this as a utility-increasing transaction.

Another example is lotteries.  It can actually be regarded as
logical on an expected-utility basis to buy lottery tickets if
you are poor.   It is clearly illogical to
do so if you are rich.  And sure enough, poor people do buy lottery tickets
much more per person than rich ones.

>> --most people are not too stupid to range-vote (or at least, do not think they are) and 
>> accomplish the task basically about as fast as they can write.

>Interesting experience, quite opposite to mine. May I ask you how they do it without having 
>to know the difference between 64 and 65 points as you suggested above?

--I do not know how they do it.  I merely know I did a range voting exit poll of 122
real-world voters in 2004, and this is what happened.  You can read about it
   http://math.temple.edu/~wds/homepage/works.html   #82.

>> For example, a decision faced by Bush soon after entering office was 
>> whether to change maximum-permitted-levels-of Arsenic-in-water standards.  Different
>> maximum arsenic levels lead to different amounts of cancer and health problems.
>> We could totally eliminate the health consequences by demanding "at most 1 atom As per
>> liter" but the cost would be enormous, and indeed if too much money
>> were devoted to this then lives would be lost for lack of money in other areas,
>> (for example mass starvation...)
>> There is an optimum choice utility-wise here.  Bush & the EPA basically attempted to find it,
>> and in my estimate (I checked the math) correctly, but they then were placed
>> under political pressure by Democrats and chose to make a revised (now wrong)
>> decision.

>I'm so glad you know what's right and wrong!

--you are trying to mock me, but it is not working.  The bottom line is, if you are
in a governmental position, then you have to make this kind of decision.  If you
act in some muddled emotional way, you will cost humanity an enormous amount of expected utility,
i.e. cause tremendous damage.  If you act in the correct way, which is to try
to estimate expected utilities of the options and pick the best one, then
you save lives.   This should not be mocked.  This should be taught in schools.
Obviously by carrying on this debate you are not directly causing harm to humanity, but
your wrong ideas continually do cause tremendous harm to humanity, and harm that
can be approximately quantified by those of us who try to estimate utilities.

To return to the voting system arena, even though utility is kind of a nonconstructive existence
creature,  the mere fact that it exists can be usefully used:  specifically it is
possible to measure the "Bayesian regret" of voting systems.  See 
   http://math.temple.edu/~wds/crv/bayregdum.txt
Mildly similarly, nonconstructive existence proofs are used al the time in mathematics
and are very useful, which is exactly why the Browuerians are nearly extinct.
wds