It is almost a mathematic impossibility for our current voting system to elect moderate candidates. All this time I thought the impasse in Congress was due to flaws in the campaign system. Actually, the campaign experts are applying strong knowledge of how our election system works. In a close election, the candidate who is capable of working with both sides will frequently lose.
Most states elect Congresspersons based on a “plurality-with-elimination” method. The candidate with the majority of votes wins the seat. If there is no majority, then a run-off election is held for the top vote getters. Sound fair? All voting methods have flaws, but plurality-with-elimination has several flaws.
The flaw that is disrupting Congress now, is that the first candidates to be eliminated are usually the moderate candidates. Here is an example: assume that Very Conservative gets 81 votes, Moderate gets 75 votes, Unheard Of gets 10 votes, and Very Liberal gets 80 votes. Further assume that voters favoring Very Conservative or Very Liberal would prefer Moderate over their arch rival. None of the candidates received a majority of the votes. Using the “plurality-with-elimination” method, Moderate (as well as Unheard Of), are eliminated from the election and a run-off election is held between Very Liberal and Very Conservative, who are incapable of acknowledging the validity of the other’s viewpoint.
I can prove mathematically why the candidate who would win in a head-to-head match-up with all other candidates, will lose the election. Well, I can’t prove it, but mathematical economist, Nobel Prize winner Kenneth Arrow proved it back in the fifties. He showed that any method for determining election results will always violate a fairness criteria–specifically the “head-to-head criteria” (winner might be a loser if compared head to head with other candidates), “majority criteria” (method will not always elect the person with the majority of win votes), the “monotonicity criteria” (I’ll ignore this one), and the “irrelevant alternatives criterion” (I’ll ignore this one as well.)
The plurality-with-elimination method can violate the “head-to-head criteria,” as well as all the criterion except “majority.” A candidate who is everybody’s second choice, even in a multi-candidate election, would lose. Consequently, our voting method almost guarantees that elected officials will be the ones least likely to compromise.
Is there another voting method that could ensure more moderate candidates? Of course there is. You see it on the newscast polls. It is called a “Pairwise Comparison.” In this method, voters rank all the candidates. Then the candidate is compared to each of his or her rivals. The candidate who wins the most pairwise comparisons and is therefore favored above all others by most of the voters, is declared the winner. In fact, the “Pairwise Comparison” method violates fewer fairness criteria than any other voting method I know of.
Good luck, however, getting the politicians who were elected to your state legislature by the plurality-with-elimination method, to change your state’s voting method.
Reference: Robert Blitzer, Thinking Mathematically, Annotated Instructor’s Edition, 5 ed., Prentice Hall (2011)