On 2/22/23 04:39, Forest Simmons wrote:

And for those who like a theoretical challenge, there's still the design
question of making a method that takes von-Neumann-Morgenstern utilities
to their logical conclusion while remaining cloneproof and dealing with
Range's strategy problems.

In a three-candidate election, we don't know if a particular voter's
9/10 is the same as another voter's 9/10. But we can infer lottery
probabilities. So each voter's ballot can be normalized to (1, a, 0) if
we use l_infinity normalization.

So we could do just a normalized Range, but this has undesirable
strategic consequences - the usual Burr dilemma, minmaxing, etc. With
different normalization types (e.g. l_2 cumulative voting) that's
mitigated but at the cost of it no longer being cloneproof (vote-splitting).

I thought that perhaps something with the logic of a Condorcet method
would work better, with, instead of pairwise contests, there would be
pairwise triples: the minimum necessary to capture strength of
preferences. But I just couldn't make it cloneproof.

-km

On 2/21/2023 7:39 PM, Forest Simmons wrote:

The concept of "recursively" would be very difficult to explain to most
voters.  (Many voters think that IRV/STV's transfer of votes is too
complex and possibly unfair.)

IMO the concept of "recursive" is even harder to explain than "pairwise"
(even if the word itself is avoided).

I believe part of their stubbornness comes from their initial belief
that IRV was the only way to count ranked choice ballots.  It's
understandable that they strongly dislike IRV (after they understood it,
which came after their initial enthusiasm for IRV).  It's mystifying as
to why they didn't realize there are lots of better ways to count ranked
choice ballots.

IMO both the STAR organization and the FairVote organization suffer as a
result of being led by people who do not fully understand mathematics.
In both cases they later worked with math-savvy experts, but only if
that math-savvy expert was willing to go along with the
already-established method.  The two leaders are slowly learning the
relevant math, but alas only after doing lots of money-backed promotion
for inferior counting methods.

I do agree with the fans of STAR voting that a voter should be allowed
to mark two or more candidates at the same preference level.

Currently I'm trying to educate local election officials that IRV can
count those marks.  And that this counting can be done without using
fractions.  (Simply "pair up" equivalent ballots, and distribute those
ballots in "whole" equal numbers to the same-ranked candidates.)

If the Portland (Oregon) elections in 2024 do count such marks --
instead of discarding them as "overvotes" -- then I'll know my local
education efforts have been fruitful.  I have my fingers crossed.

Richard Fobes
The VoteFair guy
(not to be confused with the other Richard in this forum)

(In the title I'm hoping that "guys" is intended to be the
gender-neutral version of this word to cover the election-method experts
who are female.)

On 2/21/2023 7:39 PM, Forest Simmons wrote:

But now we have a better use of score ballots ... Rob Lanphier's imperative
that whatever method we advocate should be flexible  enough to accept both
rankings and ratings ... like the engine of an Army deuce and a half that
will run on anything from salad dressing to jet fuel.

So this definition is intended to make sense with both types of ballots.

A candidates Top count is the number of ballots that do not rank or rate
any other candidate above it.

Similarly, a candidate's Bottom count is the number of ballots that do not
rank or rate any other candidate above it.

Our method is based on Robert's imperative that a nominal (tentative)
standard of "worst" can be trumped by direct democratic comparison.

For example, the Condorcet Loser, a candidate that is democratically weaker
in comparison to any other candidate is trumped by any other candidate,
nominal judgments of "worst" to the contrary not withstanding.

Candidate Y is deemed to be democratically weaker than X, if X is ranked or
rated above Y by a majority of the participating voters ... even if the
nominal/tentative standard of "worst" favors Y over X.

How strong can a candidate actually be if (according to their preference
ballots) a majority of the participating voters prefer the nominally worst
candidate over it?

We start by listing the candidates from worst to best by our nominal
standard of worst, which is the same as IRV's ... the smallest top count
... with ties decided by worst bottom count.

Then while any candidate remains on the list, strike from it the worst
remaining candidate ... after first striking any (and every) democratically
weaker candidate (if any exists).

When this elimination process has whittled the list down to one candidate,
that's the election winner.

This formulation with the top and bottom counts determined before any
candidates are stricken from the list ... makes for a method that is
(unlike IRV) a one pass, precinct summable, monotonic method.

Did I mention clone proof and ISDA?

In fact, not only Landau efficient (electing only uncovered candidated) but
Banks efficient ... the winner stands at the head of a maximal chain
totally ordered by pairwise defeat. [The other members of the chain are the
last to be stricken st each eliminationvstage.]

How does this proposal strike you?

(Not from any good list,I hope)

-Forest

On Wed, Feb 22, 2023, 4:40 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 22.02.2023 19:44, Forest Simmons wrote:

That does sound pretty good (and I may have to check it in detail, or if
it could be used to move Friendly closer to ISDA). But from a cursory
glance, if top count is used for the initial order, would it pass ISDA?
Imagine the "everybody ranks himself first as a write-in" idea: all of
the single first preference candidates are Smith-dominated, but they
completely obscure the top counts (first preferences). So the bottom
count tiebreaker would be used, which would presumably give a different
order than the top count with Smith candidates eliminated.

In any case, by referring to vNM utilities, I was thinking of methods
that take preference strength into account. Such a method must fail
Condorcet, much less ISDA. Consider the usual weak centrist vs Condorcet
winner contention point, our ordinary LCR with a very weak C-first count:

50: L>C>R
40: R>C>L
5: C>R>L

IRVists say C must lose because C is a milquetoast baby-kissing
candidate. Condorcet proponents say that C still beats everybody else
one-on-one. With preference strengths, we could theoretically
distinguish the strong centrist scenario:

50: L (9) C (8) R (0)
40: R (9) C (8) L (0)
5: C (9) R (3) L (0)

from the weak centrist:

50: L (9) C (1) R (0)
40: R (9) C (1) L (0)
5: C (9) R (3) L (0)

and elect the CW in the first scenario but not the second -- at least as
long as the method's strategic distortions aren't too severe.

(An interesting side question would be: suppose we have a two-player game:
50: L (9) C (x) R (0)
40: R (9) C (y) L (0)
5: C (9) R (3) L (0)
where the two players are the L and R factions and their moves are
choosing some value for x or y. For which lp-norm cumulative vote
methods is the Nash equilibrium significantly different for strong and
weak centrists, so that the method can tell them apart even under
strategy? I've heard that Euclidean normalization is particularly
strategy resistant, but I haven't verified this.)

-km

On 22.02.2023 22:25, Kristofer Munsterhjelm wrote:

Whoops, sorry, the numbers were wrong. That should be

50:L>C>R
46:R>C>L
5:C>R>L

and all the derived examples need to be corrected too.

-km

Richard,

Keep up the good work ... I know your work in the tranches is an up hill
battle and a thankless task.

The recursive formulation of SPE was not intended for public consumption
... only to point out to the "numerate" the irony of how tantalizingly
close STAR is to the well established, traditional Sequential Pairwise
Elimination procedure with a score based agenda. [Traditionally the SPE
agenda can be based on anything ...whim of the chair ... alphabetical order
... whatever ... it is external input to the SPE procedure.]

Keep up the good work!

-Forest

PS see my suggestion in-line below ...

On Wed, Feb 22, 2023, 9:52 AM Richard, the VoteFair guy <
electionmethods@votefair.org> wrote:

Another solution is the Martin Harper solution: two passes through the
ballots for each elimination step ... initially count the equal first
rankings as whole "equal first approvals" ... then (on the second pass)
transfer the entire vote of the ballot to its equal-first candidate with
the greatest equal-first approval total (from all the ballots).

Does that make sense?

It strengthens IRV's partial clone-winner compliance ... a definite
improvement!

The method becomes so robust that even if every voter made all their ranked
votes equal-first, this method would not break down.

The method can be thought of as a happy marriage of Approval and IRV ...
for people not put off by mixed marriages.

Very interesting questions!

With regard to the ISDA question ...

It would be very strange for most voters to use up all of their equal-first
options without including at least their favorite Smith candidate as a
compromise.

Indeed, it's hard to see how the frivolous top voting could happen without
the bottom preferences hijacking the determination of the Smith set.

But here's the way to look at it: the method is just agenda based chain
climbing in disguise.

Until you reach the worst Smith item on the agenda, everything is
irrelevant to the final outcome.

-Forest

On Wed, Feb 22, 2023, 1:25 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

There is a way to get round that problem of a compulsory last preference
helping to elect a candidate, that the voter opposes.

As you pointed out, the compulsory voting of all preferences still holds
for the Australian lower house single member districts. So, the voter is
obliged to possibly help an opponent they would never willingly vote
for. Binomial STV would put the voter back in charge, because when the
voter ranks more candidates than there are seats, the preferences start
to count more and more against candidates. Thus, a last preference may
count as much against a candidate, as a first preference counts for a
candidate. This is because Binomial STV (apparently the sole birational
voting method) consists of a rational exclusion count exactly like the
normal election count of surplus transfers, but with the preferences in
reverse order. And abolishing the traditional STV "last past the post"
eliminations, when election surpluses run out.

An exclusion count is not necessarily a negation of an election. An
elected candidate, on a quota, may not be excluded, on a quota. That is
to say a popular candidate may also be a not unpopular candidate.

All possible abstentions are allowed and all are counted (conservation
of preferences), which determines how much the voters are inclined to
elect or exclude the line-up of candidates.

Regards,

Richard Lung.

On 21/02/2023 00:11, Bob Richard (lists) wrote: