“…Therefore various sets of alternatives were proposed as solution concepts for majority voting games and/or as social choice rules. Below several such concepts are considered and compared: dominant set (Ward, 1961;Smith, 1973), minimal dominant set (Fishburn, 1977;Miller, 1977), undominated set (Ward, 1961), minimal undominated set (Schwartz, 1970(Schwartz, , 1972, weakly stable and minimal weakly stable sets (Aleskerov, Kurbanov, 1999), uncovered set (Fishburn, 1977;Miller, 1980), uncaptured and untrapped sets (Duggan, 2007). In addition we introduce a new solution concept -k-stable sets of alternativesand analyze its relations with other solution concepts listed above.…”