[EM] Message to Ernest Prabhakar

[Michael Ossipoff]

 Hi Ernest--

I want to comment on your MMV voting system, but I couldn't find your
e-mail address at your website, and I forgot the password that I chose
when I joined the website (I'm in te process of trying to fix that
situation).

So I'm posting this to EM, in hopes that you'll find it here:

Dr. Prabhakar--

In MMV as you propose it, you're dropping cycles of equal defeats too
soon. (But so was I, in my Drop-Equal-Defeats). Before dropping them,
ensure that more compellingly-dropped defeats are dropped first.

More compellingly-dropped defeats would include defeats that cycle
with stronger defeats, and defeats that cycle with a mixture of equal
and stronger defeats.

Someone at EM pointed out that, without that hierarchy, dropping
cycles of equal defeats could result in a weaker defeat being kept
while stronger ones are discarded, for no reason other than that the
weaker defeat is weaker.

He (Markus Schulze) also pointed out that that could lead to nonmonotonicity.
I admit that my Drop-Equal-Defeats (DED) proposal does exactly what
MMV does. DED wasn't a good idea.

MAM, Tideman's Ranked-Pairs, CIVS-RP, and MMV are all versions of the
general method known as Ranked-Pairs (RP).

I'd like to state, here, definitions of some RP versions, including
CIVS-RP, MAM, and my own improved version of  MMV.

My MMV, due to its hierarchial structure, is a lot more
wordily-defined than the definitions of CIVS-RP and MAM. It's so wordy
that I almost hesitate to include it, but I will anyway.

These definitions are time-independent definitions. I prefer
time-independnt definitions because they're briefer--sometimes a lot
briefer--than ordered-procedure definitions.

Here are those definitions:

General supporting definitions used in all of these definitions:

"X beats Y" means that the number of ballots ranking X over Y is
greater than the number of balots ranking  Y over X.

A defeat is instance of one alternative beating another.

The strength of a defeat is measured by the number of ballots ranking
the defeating alternative over the defeated alternative.

If two defeats are equal in that regard, then the one that has fewer
ballots ranking the defeated alternative over the defeating one is
counted as the stronger of those two defeats.

A defeat contradicts a set of defeats if it's in a cycle (e.g.
A>B>C>A) that consists only of it and them.

An alternative is disqualified from winning if it has one or more
not-discarded defeats.

Some specific RP definitions:

CIVS-RP:

A defeat is a disqualified defeat if it contradicts a set of
not-disqualified stronger defeats

[end of CIVS-RP definition]

Maximize Affirmed Majorities (MAM):

When there are equal defeats (or a final tie resulting from one or
more pairwise ties), MAM randomly chooses one of the ballots, and uses
its ranking to order the equal defeats and to solve outcome-ties
caused by pairwise-ties.

The dominance-hierarchy order of two defeats is determined by how its
defeating and defeated alternatives are ranked with respect to
eachother in the randomly-chosen ballot.

MAM:

A defeat is a disqualified defeat if it contradicts a set of
not-disqualified defeats each of which is stronger than it is, or (if
equal to it) higher than it in the dominance-hierarchy.

[end of MAM definition]

Those two definitions are so brief that I almost don't want to post my
improved MMV definiltions.

Before I start, let me comment on MAM and CIVS-RP:

MAM is probably the best. By its random hierarchy of equal defeats,
MAM, when there are equal defeats in a cycle, simulates an election
that doesn't have equal defeats. By that, I man that MAM gives the
result that would happen if those equal defeats were somewhat unequal.

In contrast, the deterministic RP methods such as CIVS-RP and MMV
(your version and mine) do something quite different. They make bigger
change in the count than MAM does, in comparison to what it would have
been without equal defeats.

I'm not saying that my MMV versions would have a problem due to that
(as does DED and the previous MMV version), but I'm not saying that
they don't. If they do, it probably isn't a serious problem, but it
probably gives an outcome that isn't quite as right as the MAM
outcome.

An objection to MAM is that mid-count randomization isn't feasibly
verifiable in Internet voting (polls and organizational). But Eppley
points ot that that isn't so. Based on the voters' rankings, according
to a pre-established and published rule, a randomizing seed-number
could be generated, and then that seed number would generate the
random number that would choose the randomly-chosen ballot.

Or, simplifying the process a bit, the random-ballot could be chosen
based on part of the remainder resulting from a division of two
numbers coming from some aspects of the voters' rankings.

In summary, mid-count randomization needn't have a verification
problem, even in Internet voting.

And look how brief MAM's defnition is. It's as brief as CIVS-RP's definition.

Though I like my MMV versions, I must admit that I recommend MAM
instead, for polling, and for other voting under ideal majoritarian
conditions

Because of the length of this post, and the length of my MMV versions,
and what i want to say about them, let me post this now, and then post
my MMV versions in a subsequent post.

[To EM: I've modified my MMV definition so that all 3 of its
paragraphs are time-independent. And I propose MMV in two versions, in
which paragraphs 2 and 3 are applied conditionally or unconditionally,
based on whether any alternative wins via defeat discards in previous
paragrahs]

Michael Ossipoff