How bad is it to use plurality voting in party primaries?

Really, really bad.

1. Richard A. Joslyn: The impact of decision rules in multi-candidate campaigns, the case of the 1972 Democratic Presidential Nomination, Public Choice 25 (1976) 1-17

Found that in fully one-third of the (many) Democratic party 1972 primaries he studied, the plurality system (that was employed) probably failed to elect the Condorcet Winner. Then Cooper and Munger did computer simulations suggesting primary results were to be expected to be practically random and chaotic:

2. A.Cooper & M.C. Munger: The (un)predictability of primaries with many candidates: Simulation evidence, Public Choice 103, 3-4 (June 2000) 337-355.

Abstract: It is common to describe the dynamic processes that generate outcomes in U.S. primaries as "unstable'' or "unpredictable''. In fact, the way we choose candidates may amount to a lottery. This paper uses a simulation approach, assuming 10,000 voters who vote according to a naive, deterministic proximity rule, but who choose party affiliation probabilistically. The voters of each party then must choose between two sets of ten randomly chosen candidates, in "closed'' primaries. Finally, the winners of the two nominations compete in the general election, in which independent voters also participate. The key result of the simulations reported here is the complete unpredictability of the outcomes of a sequence of primaries: the winner of the primary, or the party's nominee, varied as much as two standard deviations from the median partisan voter. The reason is that the median, or any other measure of the center of the distribution of voters, is of little value in predicting the outcome of multicandidate elections. These results suggest that who runs may have more to do with who wins than any other consideration.

3. And that all is very unfortunate because party primaries are tremendusly important. According to Kermit Gordon (president of Brookings Institution):

One basic truth about American politics emerged yet again from the 1972 election: presidential nominations are more important than presidential elections.

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