[Election-Methods] utility theory lesson for a very confused rob brown

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sun Jan 6 19:37:13 PST 2008

At 01:34 AM 1/5/2008, Don&Cathy Hoffard wrote:

A response taking this totally off the planet.

> >it's a proof that intensity of preference, not just order, exists.  if you
> >and i both prefer A>B>C, but I score them 10/9/0 and you score them 10/1/0,
> >then I would take the guarantee of B over the 50/50 chance of A-C.  You
> >wouldn't - unless you sucked at math.
>Let's assume that that we voted as follows:
>You voted  A>B>C   10/9/0
>I voted    A>C>B   10/1/0

There is a meaning to these votes: the first voter is adding weight 
to the election of A and B, almost the same for each, and giving no 
value to C. The second voter is giving only value to A, and 
practically none to C and I wonder why he (Don) even bothered. I 
don't expect those very low values to see much use, actually. 9, yes.

>And somehow A is eliminated (Low count by others)

Okay. But this is *during* the election count. Yet Don then treats it 
as if it is some new election.

>The election comes down to B or C, and you and I are the last two voters,
>and the count at that point has C leading by 7 votes (Count)
>Then you get to vote for B 9-times while I only get to for C 1-time
>and thus B wins by one vote (count).

Actually, Don and Clay each have one vote, which they may cast with 
respect to each candidate: A Range election is like the simpler 
Approval election, where the questions are asked, "Shall Candidate A 
be elected, shall Candidate B be elected, shall Candidate C be 
elected? With Approval, the voter may cast one vote (Yes or No) for 
each of these questions; and in some implementations, No is assumed 
if you do not vote Yes. With Range, voters can cast fractional votes; 
in this case, in multiples of 1/10 vote. But for convenience and 
simplicity of expression, the whole numbers are used, a scale of 0-10 
instead of 0-1.

The Range vote is a red herring, the same objection would be made if 
this were an Approval election with votes of 1/1/0 for ABC from Clay 
and 1/0/0 for Don. Don would then complain that he did not get to 
cast a vote for C. But he did have the opportunity to cast that vote: 
initially, and he chose not to cast it.

What *really* happened was that each voter cast *three* votes. One 
for each question presented. In the Range election, each voter may 
vote on the election of each candidate, fractional votes allowed but 
not required.

It's already standard practice in states where ballot questions are 
submitted, and where it is possible for two conflicting questions to 
appear on the ballot, that each question must get a majority Yes to 
pass; but if two get a majority, the one with the highest Yes vote 
prevails. This is essentially Approval voting (with a majority 
requirement, which I highly recommend). It's quite legal, never been 
challenged, to my knowledge.

The argument Don raised, however, was the argument accepted by the 
majority in the Minnesota Supreme Court, in the case Brown v. 
Smallwood. The result of that decision was that an election where the 
majority clearly preferred Smallwood, based on the votes, was 
reversed. The method used for election was Bucklin, which is a ranked 
Approval method. First rank, vote for one only, Second rank likewise, 
third rank, voters could vote for as many as the like. Unlike IRV, if 
there was no majority in the first round, the second round votes were 
added in, and if none yet, the third round votes were added in. I 
think it was plurality required for victory, however.

There was a dissent filed in that decision which pointed out a great 
deal of contrary precedent, that the decision was contrary to the 
great majority of legal opinion at the time, and the Minnesota 
decision contradicted another state's precedent. No other court in 
the U.S. found Bucklin unconstitutional on that ground (In fact, in 
Oklahoma, if the partial information I have is correct, Bucklin was 
struck down on the grounds that the additional votes were added in 
fractionally. I.e., second rank was added in as some fraction of a 
vote. Had it been a full vote, I think the outcome would have been different.)

Approval voting is a kind of alternate vote. By voting for A and B, 
the voter is saying "If not A, then B; if not B, then A). IRV works 
this only in one direction: If not A, then B. If not B, then C. And 
because of this, because of the candidate elimination, IRV can elect 
a candidate who would be beaten, per the expressed votes, by another 2:1.

>What happened to the concept of one-person one-vote.

It's all in how you look at it. What is the *purpose* of one-person, 
one-vote? Brown v. Smallwood was concerned about the number of marks 
on the ballot (in spite of a protest at one point that it was the 
voters who counted, not the marks). If Brown v. Smallwood stands, IRV 
will be found unconstitutional in Minnesota, I'd predict. But, more 
likely, it will be tossed out, it was a very bad decision, clearly 
reversing a popular election where the voters *counted* on being able 
to vote sincerely. If it had been a plurality election, they would 
have voted differently and quite likely Smallwood would have won.

>At least in the U.S. the Supreme Count might have something to say 
>about this election.

The Supreme Count, yes. The Duke of Florida will assist.

>You could say that your "large happiness gain" or welfare is greater 
>than my "slight disappointment loss".
>   And society is better of (i.e. Maximizing Social Welfare)

Off. Better off. What Range voting does is to equate the satisfaction 
of all voters, to assume that the satisfaction of each one is equally 
important. You decided that C was not important. Now you, apparently, 
want to complain, no, it *is* important.

>Who's to say my "slight disappointment loss" might be larger (in 
>welfare) than your "larger happiness gain".

Nobody. It's a *assumption* of democracy. One-person, one-vote, you 
know. It appears that what Don wants is to have *two* votes: He wants 
to vote A>C with a full strength vote, effectively saying *this is 
maximally important to me." But then also C>B with the same strength. 
Range requires him to limit his entire range of preference to one full vote.

You want real democratic process: elect candidates by what Robert's 
Rules actually recommends: multiple rounds, *no* eliminations. 
Approval simply does that by compressing it a bit, at some cost. 
(That is, it's possible that the majority preferred A but Approval 
elects B -- but only if the majority also approved B, and, perhaps 
not realizing their position, in larger numbers. It's certainly not a 
bad outcome in that case!) In real elections, multiple majorities 
would be rare, especially in a basically two-party system. In 
primaries, they would be common. Faced with an Approval Democratic 
primary right now, I might actually approve five candidates. And 
would truly be happy to see the one most widely approved win.

In a U.S. Presidential election, say if it had been Florida 2000, how 
many people would have approved both Gore and Bush? And that is what 
it would take for both to get a majority, quite a few such voters, 
and an absence of third party candidates. (In fact, people now do 
vote like that, a certain percentage of ballots will have both 
candidates in a two-party election marked. And the result is the same 
as in Approval: no net effect....)

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