[EM] MDDA: prefer deluxe, evaluate properties

[Warren Smith]

MDDA *if* all votes are full rank orderings, is just the "Smith set"
and often yields a tied election.  In fact often the Smith set is the entire
set of candidates.  (In most of Australia full rank orderings - i.e. none omitted -
are demanded by law.)

This seems a severe problem with MDDA and probably is a good reason to prefer
"Deluxe MDDA" which will (in the limit of a large number of voters and with some randomness)
generically not be tied, even with all voters expressing maximum information.  

Properties of Deluxe MDDA:
It is fairly simply defined, though not as simple as range voting.

Deluxe MDDA seems plainly monotonic in both senses (ranking and approval thresh) simultaneously.

It elects a Condorcet Winner if one exists.

It refuses to elect a Condorcet loser.

It is generically untied.

It is Clone-immune.

It is "additive" i.e. precincts can only send in "subtotals" to central tabulators
and that suffices to compute the results (there is a subtotal for each
candidate-pair and another approval-count for each candidate singleton). (Unlike IRV.)

MIke Ossipoff recently claimed Deluxe MDDA satisfies FBC, SFC, and SDSC.

Those things were all good.  Now for some bad properties:

It is not doable on dumb-plurality-totaling voting machines, unlike range voting.
(For example, no way such a machine could check ballot-validity, i.e. acyclicity.)

It does NOT satisfy subdistrict consistency, that is, if district 1 elects winner W
and so does disjoint district 2, that does not imply that the combined winner is W.

It does NOT satisfy incentive to participate, in the sense that you can be better
off by "not showing up" to vote, because your honest vote can actually hurt you.

It fails "add top", i.e. adding votes all ranking A top, can harm A.

All of the last three failures happen automatically by theorem for essentially any
Condorcet method, and Deluxe MDDA is just a Condorcet method if all voters approve
or disapprove all candidates (or anyway if all approval counts are tied) enabling
you to re-use the same counterexample elections to show them.

Finally, consider what I call the "DH3 scenario" 
   http://math.temple.edu/~wds/crv/DH3.html .
This is a horribly-common and horribly-severe problem that Borda and all Condorcet methods
based on full-ranking-ballots suffer from in the presence of strategic voters.  
But Deluxe MDDA might be able to avoid it because it is not just a 
ranked-ballot method - there are also those approval threshholds.  Let's see.
The situation is there are 3 main rival candidates A,B,C with comparable 
support, and a "dark horse" D whom all feel is inferior and has "no chance."
The pathology is the A-supporters strategically rank A>D>B&C
and so on (although they honestly feel  A>B&C>D), resulting in D winning.
With Deluxe MDDA, they presumably still will act that way, BUT only approving
the top one and disapproving the bottom three.  In that case D is the Condorcet
winner and wins despite zero approval.  So it appears Deluxe MDDA still suffers
from the horribly-common and horribly-severe DH3 pathology.  

This DH3 failure is a very bad
thing and would severely increase its Bayesian Regret.
 
wds