[EM] u/a for criteria. u/a FBC. Voter's Choice. SSCS. Strong FBC.

[Michael Ossipoff]

Of course the way to define u/a for criteria would be in terms of votes.

A definition of u/a for criteria:

In a critrerion failure-example, an election is u/a for some particular
voter V iff:

The candidates can be divided into two sets, A and B, such that V votes all
of the candidates in A over all of the candidates in B, and doesn't vote a
preference
within A or B unless the failure-example critrerion-writer can prove
conclusively that it isn't possible to contive a configuration of ballots
other than that of V, such that:

.....V, by voting that particular preference within A or B, causes the
winner to come from set B, where the winner would have come from set A if V
hadn't voted
.....that paraticular preference within A or B.

[end of definition of u/a for criteria]

An election is All-u/a if it is u/a for every voter in that election.

[end of All-u/a definition]

A tentative definition of u/a FBC:

In an All-u/a election, FBC should never be violated.

[end of tentative definition of u/a FBC]

To questions suggest themselves:

1. Does compiance with u/a FBC guarantee that there won't be a
societally-damaging favorite-burial incentive?

2. Do Smith-Approval and Smith-Top meet u/a FBC?


Voter's Choice:

I'm going to refine my definition of Voter's Choice, but first let me
summarize what I've already said:

The Voter's Choice definition that has a voter's ballot giving a point to
the winner by that voter's designated method, and also to every
candidate ranked higher on hir ballot, has two problems:

1. It spoils the defection resistance of ICT and Smith-Top.

2. It legislates Approval to a degree that could be considered unfair by
non-Approvalists.

So I prefer the definition that merely says:

Voters may designate a method. The methods are weighted according to how
many people have designated them.

In other words, each candidate receives a point for each voter who has
designated a method that elects that candidates.

[end of previous Voter's Choice definition]

It occurred to me that if there are two good methods that you feel will
give a good result, and you like one more than the other, but that other
is likely to have more support from others, then there could be the
familiar split-vote problem, for deciding which method to designnate.

So then, why not let voters designate more than one method?:

I'll now call this Voter's Choice 2:

A voter may designate one or more methods.

The methods are weighted according to the number of people who have
designated them.

In other words, each candidate receives a point for each voter who has
designated one or more of the methods that have chosen hir.
The candidate with the most points wins.

[end of Voter's Choice 2 definition]

I think that Voter's Choice 2 is considerably better than Voter's Choice.
I'll probably soon say that Voter's Choice 2 is what I ;mean
by "Voter's Choice". But, since Voter's Choice 2 is a new proposal, then,
for now, I'll leave them with those two different names.

For EM polls, or even for public elections,  whenever it's desired to make
a choice when there is no one established method,
then Voter's choice 2, or maybe Voter's Choice, would be the best way to
make that choice.

SSCS:

I now claim that SSCS says something that _is_ of interest. It speaks of
whether or not, when making Compromise win instead of Worse
is the only way to defeat Worse, and when there is a way that you can vote
that will achieve that, you have a specific simple way of voting
that will achieve that.

Approval and Abucklin (in all of its versions) are the only methods that
have even been claimed to meet SSCS.

Also, no one has suggested that any method other than Approval can meet
Strong FBC.

By the way, speaking of Approval and criteria, it's been some time since I
looked at Arrow's criteria, but it seems to me that the only
one of those that Approval fails is a _rules_ criterion, as opposed to a
_results_ criterion. It's a "criterion" that requires that the method be
a rank method.

I have no use for rules "criteria".

I could be mistaken, because I haven't looked at Arrow's criteria for a
long time.

Mike Ossipoff




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