[EM] NESD and NESD* properties of a single-winner voting method

[Warren Smith]

To formalize something pretty well known by now as a "property":

A single-winner voting system "fails the NESD property" if, when every
honest voter
changes their vote to rank A top and B bottom (or B top and A bottom;
depends on the voter which way she goes), leaving it otherwise
unaltered, that always (except in very rare "exact tie" situations)
causes A or B to win.

Presumably voting systems failing NESD will generally lead a country
into 2-party domination.

Systems failing NESD:
IRV (instant runoff voting), plurality, and all Condorcet systems.
By these I mean, with pure-rank-order ballots (no rank-equalities permitted).

Systems passing NESD:
Borda, approval and range voting.

However: Borda restricted to 3-candidate elections fails NESD.

If we modify IRV to permit rank equalities by counting a ballot with K
candidates co-equal top as 1/K votes for each, then this system passes
NESD, although I still feel uncomfortable about it because being
co-equal top is plainly a lot worse and more vulnerable than being
sole-top (there is kind of a "discontinuity," unlike in range voting
where it is "continuous" as you cross the top score), so strategic
voters might not do the former.

To make an analogy, plurality voting with "equal votes" permitted
(i.e. you can vote "half" for Jefferson and "half" for Adams) would
clearly be stupid, i.e. would clearly be essentially equivalent
strategically to plain plurality.   Consider each of your half-votes
one at a time.  If for the first, your best move was to vote
Jefferson, then for the second, the same reasoning would apply. Hence
you'd vote 100% for Jefferson and never use the equality feature
(unless you were a strategic idiot).   But anyway, Plurality with
equals permitted, does technically pass NESD.

If we consider Condorcet systems with rank-equalities permitted, these
pass NESD but
again there is that worrying "discontinuity."

One might define the "NESD*" property to be the same as NESD except A
and B are to be SOLE-top-rated or ranked by all voters.  Then

Fail NESD*:
IRV, plurality, Condorcet (all with rank-equalities permitted or
forbidden, both work).

Pass NESD*:
Range voting.

NESD* not applicable: Approval voting.


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
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and
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