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 "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info