Selecting Among Equivalent Options: A Superior Rule to Coin Tossing in Pairwise Comparisons

Abstract

[Abstract]: In traditional decision-making, when faced with a choice between two seemingly equivalent options, a common approach is to resort to a random decision, such as a coin toss. However, this paper proposes deterministic rules that outperform such stochastic methods by achieving the same expected value while minimizing variance. Furthermore, we demonstrate numerically that, for a reasonable number of choices, our proposed rule second-order stochastically dominates the coin-tossing approach. Consequently, risk-averse decision-makers may prefer our deterministic method over traditional coin tossing.