It is proved that every strategy-proof, peaks-only or unanimous, probabilistic rule defined over a minimally rich domain of single-peaked preferences is a probability mixture of strategy-proof, peaks-only or unanimous, deterministic rules over the same domain. The proof employs Farkas' Lemma and the max-flow min-cut theorem for capacitated networks.
|Place of Publication||Maastricht|
|Publisher||Maastricht University, Graduate School of Business and Economics|
|Publication status||Published - 1 Jan 2013|
|Series||GSBE Research Memoranda|
Peters, H. J. M., Roy, S., Sen, A., & Storcken, A. J. A. (2013). Probabilistic strategy-proof rules over single-peaked domains. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 040 https://doi.org/10.26481/umagsb.2013040