[EM] Reply to D. Gamble

[MIKE OSSIPOFF]

D. Gamble wrote:

Forrest Simmons wrote in part:

>More to the point of this thread (Testing 1,2,3) if we are going to
>compare various methods, some of which are based on CR ballots and some of
>which are based on ranked preference ballots, the simulations need some
>common denominator.  Since it is easy to convert CR ballots to ranked
>ballots, and problematic to go from ranked to CR, it would seem more
>natural to use CR ballots as the common denominator.

This sounds like quite a good idea. I do see one or two potential problems
with it though:

1/ How from a CR ballot do you determine the ranked ballot truncation point 
(
the level of utility at which voters cease ranking candidates).

I reply:

Sincere rankings don't truncate. There's no need to truncate wv Condorcet 
rankings unless it's believed that someone else is going to attempt 
offensive order-reversal strategy. If a simulation is based on sincere 
voting, then have each ballot rank all of the candidates.

You continued:

I know that you've made several posts on the subject of converting CR 
ballots
into Approval ballots could you tell me where they are?

I reply:

In Approval, in a 0-info election, an election in which voters don't have 
information about eachother's preferences, or about the winnability of the 
candidates or the probability of various ties or near-ties, the 
expectation-maximizing strategy is to vote for all of the candidates whose 
utility is above the mean.

So, for each CR ballot, find the mean of the points assignments that it 
gives to all the candidates, and have that voter give an Approval vote to 
every candidate whom that CR ballot rates higher than the mean.

You continued:

Just a quick point, comparing different 'flavours' of Condorcet is actually
very boring as Condorcet cycles are fairly rare unless you produce data sets
based on unrealistic preferences within the electorate.

I reply:

No, unrealistic preferences aren't needed. All it takes is:

1. Multidimensional issue-space. With more than 1 important issue, and with 
the different issues not strongly correlated, it certainly doesn't require 
unrealistic preferences to make a circular tie.

(Of course I agree that in our elections a 1-dimensional issue-space is a 
good approximation, because the issues tend to be strongly correlated).

2. Truncation. In every rank-balloting election that I've participated in or 
conducted, there was truncation. Sometimes much truncation. Truncation can 
cause a circular tie even if there wouldn't have been one with complete 
rankings.

Truncation needn't be strategally-motivated. If there are lots of 
candidates, the voter might not bother to rank them all, only the more 
favorite ones. Maybe the voter is in a hurry because s/he has a  lot to do 
that day after voting or has to be somewhere soon. Some people will refuse 
to rank candidates who are really repugnant to them. Some people won't want 
to rank a candidate who is a rival to their favorite. That voter might not 
want to help that candidate be CW. At one election someone said "I don't 
have to vote between those 2".

So circular ties aren't inconceivable at all. WV and margins differ 
drastically in how well they deal with circular ties resulting from 
truncation or offensive order-reversal.

With wv, truncation can't steal the election from a CW whom a majority rank 
over the truncators' candidate.

With wv, offensive order-reversal can be deterred by defensive truncation.

Interestingly, these properties are shared by NES, Nash Equilibrium 
Selection.

Apparently NES meets SFC, GSFC, WDSC, & SDSC, though that hasn't been 
rigorously proved.

A preliminary example suggests that DSV and Ballot-By-Ballot are likely to 
have those properties also.
Those methods might well have the same strategy properties as NES.

DSV & Ballot-By-Ballot should be thoroughly studied in examples with 
offensive truncation, offensive order-reversal,  and offensive 
order-reversal countered by defensive truncation. Maybe computer simulations 
are the only way to study those complicated methods.

The criteria SFC, GSFC, WDSC, & SDSC describe some advantageous strategy 
properties. WV meets those criteria. Margins doesn't meet any of them.

Mike Ossipoff

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