Arrow's impossibility theorem demonstrates that any move beyond Pareto to richer social welfare functions requires either dictatorship or violation of independence of irrelevant alternatives, making Pareto's silence a rational boundary rather than a defect.

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Arrow's impossibility theorem(as cited to demonstrate limitations of voting systems): A famous mathematical proof by economist Kenneth Arrow showing that no voting system can be perfectly fair—every method has some flaw or contradiction when you try to satisfy multiple fairness goals at once.
Dictatorship(as used in social choice theory): In this context, a voting or decision system where one person's preferences always win, no matter what anyone else wants.
Independence of irrelevant alternatives(Social choice theory / welfare economics; formal constraint on aggregation functions mapping individual welfare profiles to social orderings): A condition on a social welfare function F such that for any two preference profiles over a domain, if all individuals assign the same welfare values to alternatives x and y in both profiles, then the social ranking of x relative to y must be identical across both profiles — i.e., the social ordering of any pair depends only on individual welfare levels for that pair, not on welfare levels for other alternatives.

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