[EM] A "top 3" to replace the "top 2"

[Dick Burkhart]

Oregon is considering a "top 2" primary, a very regressive move in my opinion.

So I thought what would be simplest "top 3" method that would give voters more choices, especially in regard to independent or minority candidates or parties. Less partisanship would be an added bonus.

Below is a draft answer. Effective and simple, except for the modest complexity needed to counter strategic voting.

Dick Burkhart, Ph. D., President, Democracy Works
4802 S Othello St,  Seattle, WA  98118
206-721-5672 (home)  206-851-0027 (cell)
dickburkhart at comcast.net

There is a better way than the top two primary. The top two effectively eliminates third party and independent candidates, sometimes even the second party candidate, as in Washington State’s 4th congressional district in 2014. In fact we could get rid of the primary altogether. Just rank your top 3 candidates and tally the corresponding points.

How would this work? In the standard case, a voter’s top candidate gets 3 points, the second place candidate 2 points, and third place 1 point. So imagine a Democrat, a Republican, and an Independent running against each other. Then a well regarded independent could win with only 25% backing. 

How?  Democrats would rank the Democratic candidate first, the Independent second, and the hated Republican third. Republicans would do the same, except putting their candidate on top, with the hated Democrat last. Independents would rank their candidate first and split their second and third choices between the Democrat and the Republican (so each would get an average of 1.5 points per ballot). Then if the Democrats and the Republicans split the vote with 37.5% each, the number of points counted for the Democrat would be 3*.375 + 1*.375 + 1.5*.25 = 1.875 times the size of the electorate. The Republican would have the same point total, whereas the Independent would win with 2*.375 + 2*.375 + 3*.25 = 2.25 times the size of the electorate.

This kind of calculus would provide a strong incentive for the political parties (or advocacy groups) to lessen the mud slinging or form alliances. The result: more moderate candidates, less political gridlock, and more minority candidates.
However, this standard form, which is called a restricted Borda Count, may be subjected to clever voting strategies. The first strategy is for a candidate to ask his or her supporters to rank no other candidates, so that the whole thing degenerates into ordinary plurality voting. To counter this tactic we adopt a penalty method, called the Modified Borda Count: If a voter ranks only 1 candidate, then that candidate gets only 1 point, instead of 3. If only 2 are ranked, they get 2 points and 1 point respectively, instead of 3 and 2.

A second strategy would be for candidate A to recruit 2 friends or allies to put their names on the ballot without actually running campaigns. Then candidate A would tell supporters to rank A first and the 2 friends second and third. This tactic may be nullified by an elimination strategy. When there are more than 3 candidates, we first eliminate the one with the fewest points, then next fewest, etc., until we are down to 3 candidates. In the process the number of points assigned by each ballot to each candidates is fractionally adjusted by the computer. 

Here the algorithm gets more intricate. If the eliminated candidate was third ranked by a ballot, then that 1 point would be divided up equally among the remaining candidates, except for the 1st and 2nd ranked candidates. If the second ranked candidate is eliminated, then the third ranked candidate takes its place, getting 2 points, with the extra point being distributed equally among the unranked candidates as before. If the top ranked candidate is eliminated, then the second and third place candidates are moved up, getting 3 and 2 points respectively, with the extra point again distributed equally among the remaining unranked candidates. If an unranked candidate with a fractional number of points is eliminated, then that fraction is divided up equally among the remaining unranked candidates. 

The end result of all this is that the recruited friends of candidate A will usually be eliminated, unless the other voting blocks are just too small, with the other 2 surviving candidates getting an equal number of points from candidate A’s voters. Thus candidate A will have lost all leverage that might have come from forming alliances or being strategic about ranking the other viable candidates.