Optimizing hedonic editing for multiple outcomes: an algorithm

We study hedonic editing principles that aim to find individuals’ maximum utility when confronted with multiple outcomes Thaler (Mark Sci 4:199–214, 1985). These principles have been primarily defined and studied for only two outcomes. However, when dealing with more than two outcomes, the principles become more ambiguous, and some of them may not continue to be valid. To address this, we present an algorithm designed to find the best solution over a partition set of a given vector of n outcomes. We demonstrate that this algorithm identifies the best-majorized vector for up to four outcomes and establish the conditions under which this vector is optimal for n outcomes. Our algorithm is fast since it requires at most \(n-1\) $n-1$ steps. We provide a detailed analysis of the algorithm’s performance, characterizing the conditions that guarantee the optimal solution and identifying cases where the algorithm may not converge to the optimal solution. Nevertheless, in these cases, we demonstrate through numerical analysis that it can find the optimal solution with a high accuracy rate in most ’practical’ instances, making it a reliable tool for solving hedonic editing problems.