arXiv subjects
Publications and source records attributed to Alan D. Miller.
I propose a model of aggregation of intervals relevant to the study of legal standards of tolerance. Seven axioms: responsiveness, anonymity, continuity, strategyproofness, and three variants of neutrality are then used to prove several important results about a new class of aggregation methods called endpoint rules. The class of endpoint rules includes extreme tolerance (allowing anything permitted by anyone) and a form of majoritarianism (the median rule).
We cardinally and ordinally rank distribution functions (CDFs). We present a new class of statistics, maximal adjusted quantiles, and show that a statistic is invariant with respect to cardinal shifts, preserves least upper bounds with respect to the first order stochastic dominance relation, and is lower semicontinuous if and only if it is a maximal adjusted quantile. A dual result is provided, as are ordinal results. Preservation of least upper bounds is given several interpretations, including one that relates to changes in tax brackets, and one that relates to valuing options composed of two assets.
We characterize decreasing impatience, a common behavioral phenomenon in intertemporal choice. Discount factors that display decreasing impatience are characterized through a convexit y axiom for investments at fixed interest rates. Then we show that they are equivalent to a geometric average of generalized quasi-hype rbolic discount rates. Finally, they emerge through parimutuel preference aggregation of exponential discount factors.