# Solvent comments on Imperfect Voting Systems

• Do these sys­tems avoid the strate­gic vot­ing that plagues Amer­i­can elec­tions? No. For ex­am­ple, both Sin­gle Trans­fer­able Vote and Con­dorcet vot­ing some­times provide in­cen­tives to rank a can­di­date with a greater chance of win­ning higher than a can­di­date you pre­fer—that is, the same “vote Gore in­stead of Nader” dilemma you get in tra­di­tional first-past-the-post.

In the case of the Sin­gle Trans­fer­able Vote, this is sim­ply wrong. If my prefer­ences are Nader > Gore > Bush, I should vote that way. If nei­ther Bush nor Gore have a ma­jor­ity, and Nader has the least num­ber of first prefer­ences, my vote con­tributes to­wards Gore’s to­tal. In no way does vot­ing Gore > Nader > Bush in­stead help Gore (in the case where Nader ob­vi­ously has a small num­ber of votes), but it does make it less likely that Nader will get elected, which I pre­sum­ably don’t want.

The link de­scribes how if your prefer­ences are A > B > C > D, it is some­times best to vote C > A > B > D be­cause this will help get A elected, which is differ­ent to vot­ing Gore ahead of Nader to get Gore elected.

• What about this situ­a­tion: You and your friend are the last peo­ple to vote (hav­ing the same prefer­ences for Nader over Gore over Bush) while the stand­ings are:

• 1,000,001 votes Gore first, Bush second

Giv­ing your two votes to Nader first + Gore sec­ond would mean that Gore is elimi­nated and his votes now sup­port Bush, which gets Bush elected. If you in­stead vote Gore first and Nader sec­ond, Bush is elimi­nated and his votes are trans­ferred to Nader who gets elected, which is much bet­ter out­come re­gard­ing your prefer­ences.

• You’re right. My mis­take. The stan­dard “that doesn’t re­ally ap­ply for real world situ­a­tions” ar­gu­ment of course ap­plies, with the cir­cu­lar prefer­ences and so on.

• The stan­dard “that doesn’t re­ally ap­ply for real world situ­a­tions” ar­gu­ment of course applies

I am not sure. Quite a re­al­is­tic, al­though a bit differ­ent situ­a­tion may be this: There are three can­di­dates—White, Gray and Black. White and Black are op­posed to each other while Gray is some­where in­be­tween. Thus the prefer­ences of White sup­port­ers are W > G > B and the prefer­ences of Black sup­port­ers are B > G > W. The Grays are split equally be­tween G > B > W and G > W > B.

Now sup­pose that the dis­tri­bu­tion of sup­port­ers is 40 for White and 30 − 30 Gray and Black. You are a White sup­porter. If you vote ac­cord­ing to you real prefer­ences, i.e. first W, sec­ond G, you make it likely that Gray makes it to the sec­ond round where he wins due to the trans­ferred Black votes. So you should in­stead vote tac­ti­cally first B, sec­ond W, which would help Black into the sec­ond round where he will be elimi­nated by White who has stronger over­all sup­port.

• That’s not a safe strat­egy with less than perfect in­for­ma­tion. If as few as 5 of those gray-sup­port­ers vote black sec­ondary when you thought they’d vote white, you’ve just handed the elec­tion to your worst en­emy, when by vot­ing hon­estly you could have had the mod­er­ate, agree­able-to-all can­di­date.

As a wider as­sort­ment of fringe par­ties be­come in­volved, per­haps em­bold­ened by their non­neg­ligible first-round num­bers, that sort of strat­egy be­comes more sen­si­tive to sec­ondary (and ter­tiary, etc.) prefer­ences. As part of that same in­creas­ing com­plex­ity, sec­ondary prefer­ences be­come more difficult to mean­ingfully sur­vey in ad­vance.

• Sure, but you can be nearly in­differ­ent be­tween Gray and Black, or sim­ply take the risk.