Extensions of the Young and Levenglick result about the inconsistency of Condorcet voting correspondences

The Young’s Consistency property means that when some candidates are chosen as winners by two disjoint electorates, those and only those candidates are chosen in the aggregated electorate. We define two new properties requiring that, when a candidate x is elected in a situation and a new electorate is added for which x is a very good candidate, x will remain elected. These properties, weaker than Young’s Consistency, lead to new impossibility results strengthening the Young and Levenglick result about the inconsistency of Condorcet Voting Correspondences. Also we adapt the Young and Levenglick result to the k-choice voting function context.