tl; dr When we collectively evaluate research proposals, we can reach the opposite verdict depending on how we aggregate the individual evaluations, and that’s a problem, and nobody seems to care or provide guidance how to proceed. Imagine that three judges need to reach a verdict together using majority rule. To do that, the judges have to decide independently if each of two factual propositions related to the suspected crime is true. (And they all agree that if and only if both propositions are true, the defendant is guilty). The distribution of the judges’ beliefs is given in the table below. Judge 1 believes that both propositions are true, and as a result, considers the conclusion (defendant is guilty) true as well. Judges 2 and 3 consider that only one of the propositions is true and, as a result, reach a conclusion of ‘not guilty’. When the judges vote in accordance with their conclusions, a majority finds the defendant ‘not guilty’. Proposition 1 Proposition 2 Conclusion Judge 1 true true true (guilty) Judge 2 false true false (not guilty) Judge 3 true false false (not guilty) Majority decision TRUE TRUE FALSE (not guilty) However, there is a majority that finds each of the two propositions true (see the last line in the table)! Therefore, if the judges vote on each proposition separately rather than directly on the conclusion, they will have to find the defendant ‘guilty’. That is, the judges will reach the opposite conclusion, even though nothing changes about their beliefs, they still agree that both…

Research Design Matters