[EM] Lomax continues to be confused about DH3 and range voting

[Warren Smith]

It is not possible for me to unconfuse somebody this massively confused.
I will therefore only point out a few things.

1. Lomax claims DH3 is a fantasy not seen in a real election & demands I cite a historic
example.  Perhaps that is because there has never been a real election held using Condorcet
methods.  Could that be it?   There have been Borda elections in Kiribati, whose
newspapers are unfortunately rather inaccessible to me, but I did read a polysci paper
documenting the DH3-like phenomenon that occurred in the very first election they tried.
It appears that Kiribati then abandoned the Borda system and
went back to the (superior because it is immune to DH3) plurality system and
now has 2-party domination.
http://www.electionworld.org/kiribati.htm

2. Lomax then attempted to claim Range Voting also would suffer DH3.  He
gave an "example" in which voters who favor A,B,C and not D, decide
strategically to range-vote in the style A=10, B=C=0, D=4, causing D to win.
Of course this was actually nonstrategic because D=0 was strategic.
Lomax then "explains" this by saying D was not known by the voters to be worse
than A,B,C (which was the DH3 scenario, he is therefore changing it); instead
D was "unknown" and the D=4 was a voter-guess.  Well, then D winning was not such a
disaster, was it?  Disaster=worst one wins;   Not as bad=unknown wins.
Voters would in fact only rate D=4 after A=10, B=C=0 if they thought D was in fact
likely to be superior to B,C; there is no reason to act otherwise.
Anyhow in practice my polls show that real human range voters rate unknowns as 0 rather
than as "unknown" by about a 1.7:1 ratio, so in fact, Lomax's example
would not occur.  So his example both would not occur and if it did would
not be an example.  I wish Lomax would think before blogging, rather than the
other way round.

3. Lomax mutters about voters and Condorcet cycles and how he thought it
unlikely the voters would act in a DH3 manner in view of the unlikelihood of cycle breaking.
There may be something to that, although I doubt it.
However, I am afraid I consider it much more likely
that if you ask a random real human voter "what is a Condorcet cycle" they will not know.
Given that, it seems to me unlikely that voter thinking will be dominated by Lomax's
thinking, and plausible that voters will simply act in a DH3 manner.  However, I
guess the only way to be sure is to conduct psychological experiments using real stakes,
i.e. nontrivial money.   For example, you could do something like this:
  A = everybody gets $50, but if your name starts with a letter in the first third of
the alphabet, then you get $500.
  B, C = defined similarly.
  D = $0.
Define Schulze beatpath voting, define A,B,C,D,
present this scenario to voters one by one voting by secret ballot, and say you will
tote up the election results in 1 more day, then hand out the prizes if any.
See what rank-order votes happen.   Try again with different numbers of Ds, like D1,D2,D3
to see how that affects it.

4. Finally, Lomax attacks my theorem about strategy in range voting
by asking "but what if they [voters] exaggerate?"
I  will simply allow the incredible stupidity of this "question"
and Lomax's subsequent "argument" to speak for itself.
The best I can imagine as an explanation is that Lomax has no idea what the word "strategy"
means in voting theory.  Again, I would suggest learning the word before writing 10 pages of
blogs about it, rather than after.

At some point, one tires.

wds
DH3 web page = http://math.temple.edu/~wds/crv/DH3.html
part of te CRV web page  http://math.temple.edu/~wds/crv/RangeVoting.html