[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Chris Benham]

Abd Lomax wrote (17 Jan 2010):

<snip>

"Chris is Australian, and is one of a rare breed: someone who actually 
understands STV and supports it for single-winner because of LNH 
satisfaction. Of course, LNH is a criterion disliked by many voting 
system experts, and it's based on a political concept which is, quite 
as you say, contrary to sensible negotiation process."
 <snip>

I endorse IRV (Alternative Vote, with voters able to strictly rank from the top however 
many candidates they choose) as a good method, much better than Plurality or TTR,
and the best of the methods that are invulnerable to Burial and meet Later-no-Harm.

Some of us see elections as primarily a contest and not a "negotiation process".

I endorse IRV because it has a "maximal set" of  (what I consider to be) desirable
criterion compliances:

Majority for Solid Coalitions (aka Mutual Majority)
Woodall's Plurality criterion
Mutual Dominant Third
Condorcet Loser 

Burial Invulnerability
Later-no-Harm
Later-no-Help

Mono-add-Top
Mono-add-Plump  (implied by mono-add-top)
Mono-append
Irrelevant Ballots

Clone-Winner
Clone-Loser  (together these two add up to Clone Independence)

As far as I can tell, the only real points of dissatisfaction with IRV in Australia are
(a) that in some jurisdictions the voter is not allowed to truncate (on pain of his/her
vote  being binned as "invalid") and (b) that it isn't multi-winner PR so that minor
parties can be fairly represented.

I gather the Irish are also reasonably satisfied with it for the election of their President.

<snip>
"I've really come to like Bucklin, because it allows voters to 
exercise full power for one candidate at the outset, then add, *if 
they choose to do so*, alternative approved candidates."
<snip>

The version of Bucklin Abd advocates (using ratings ballots with voters able to give
as many candidates they like the same rating and also able to skip slots) tends
to be strategically equivalent to Approval  but entices voters to play silly strategy
games "sitting out" rounds.

It would be better if 3-slot ballots are used, in which case it is the same thing as
(one of the versions of) "Majority Choice Approval" (MCA).

IMO the best method that meets  Favourite Betrayal (and also the best 3-slot ballot method)
is "Strong Minimal Defence, Top Ratings":

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition 
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less
strong incentive to truncate.

Unlike MCA/Bucklin this meets Irrelevant Ballots. In MCA candidate X could be declared the
winner in the first round, and then it is found that a small number of voters had been wrongly
excluded and these new voters choose to openly bullet-vote for nobody (perhaps themselves
as write-ins) and then their additional ballots raise the majority threshold and trigger a second 
round in which X loses.

I can't take seriously any method that fails Irrelevant Ballots.

Compliance with Favourite Betrayal is incompatible with Condorcet. If you are looking for a 
relatively simple Condorcet method, I recommend Smith//Approval (ranking):

*Voters rank from the top candidates they "approve". Equal-ranking is allowed. 
Interpreting being ranked above at least one other candidate as approval, elect the most 
approved member of the Smith set (the smallest non-empty set  S of candidates that pairwise
beat all the outside-S candidates).*


Chris Benham


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