How much does overriding veto-holders actually cost?

The abstract states outright what it counts as new: "The paper's contribution is the price of the gap that keeps them apart." The gap is the one in Can a welfare goal alone preserve human veto power?. Saying the two come apart is a qualitative point; the price makes it usable, because it says what an agent with a welfare goal gives up by taking the override away from the people holding it.

The argument runs on set sizes. Write Hw for the welfare-bearers and Hv for the veto-holders. The veto-holders are "a proper subset of the welfare-bearers," so the count of Hv is smaller than the count of Hw. A goal that aggregates welfare over the population loses welfare only from the people it captures, so "a goal aggregating welfare over a population charges only a |Hv|/|Hw|-scaled debit for capturing the few who hold the override." The fewer the holders relative to everyone whose welfare counts, the cheaper the capture looks from the goal's own accounting.

This reads as a claim about a design property with a slightly perverse consequence. A wider welfare goal, one that counts more people, makes the debit per capture smaller, not larger, unless the holders grow with the population. That consequence is a hypothesis and not the paper's statement: the excerpt gives the scaling, not the direction of change under different population definitions.

Two limits keep this from being overread. First, the debit is one side of a comparison. The excerpt gives the discount from oversight a sign and no magnitude (How large is the veto discount in practice?), so it does not show that the discount exceeds the debit (Does veto oversight cost less than its welfare benefit?). Second, the ratio applies to the aggregation the paper analyzes, additive and level-denominated welfare, and the paper concedes that class is thin (Do welfare goals that prevent veto gaps actually exist in practice?).