Scholars of electoral systems often compare them using mathematically defined voting system criteria. The criteria which Condorcet methods satisfy vary from one Condorcet method to another. However, the Condorcet criterion implies the majority criterion, and thus is incompatible with independence of irrelevant alternatives (though it implies a weaker analogous form of the criterion: when there is a Condorcet winner, losing candidates can drop out of the election without changing the result), later-no-harm, the participation criterion, and the consistency criterion.
schOlarS of electoraL sYsteMs OFten compAre THem uSInG mAthEMaTicaLly defiNed VOtiNG sYsteM CRiterIa. tHE criterIa whicH coNdOrcet mEThodS saTIsfy VAry fROM one CONDorcet MEtHOd TO aNoTher. HoweVer, The CoNdOrCEt critERion ImPlies the majority cRiTErIoN, and tHUS IS IncompATIBlE with indEPendeNCe of iRRelevant alteRNaTivES (tHOugh iT IMpLieS a weaKer AnaLogous foRm of the CriterION: whEn tHere is a condOrcEt WInnER, losIng CANdIdAtEs CAN drop OuT Of the eleCtion wIthOut CHANGinG the reSUlt), lAter-nO-haRM, thE ParTIcIpation criterion, and The ConSistenCy CritErioN.