arXiv subjects

Alessandro Arlotto

Publications and source records attributed to Alessandro Arlotto.

12 recordsLinked to original sources

arXiv2025

Ballot Design and Electoral Outcomes: The Role of Candidate Order and Party Affiliation

We develop a causal inference model to study how designing ballots with and without party designations impacts electoral outcomes when partisan voters rely on party-order cues to infer candidate affiliation in races without designations. If the party orders of candidates in races with and without party designations differ, these voters might cast their votes incorrectly. We identify a quasi-randomized natural experiment with contest-level treatment assignment pertaining to North Carolina judicial elections and leverage double machine learning to accurately capture the magnitude of such incorrectly cast votes. Using precinct-level election and demographic data, we estimate that 12.0% (SE: 3.6%) of Democratic partisan voters and 15.4% (SE: 4.0%) of Republican partisan voters cast their votes incorrectly due to the difference in party orders. A placebo test using judicial races with party designations shows that the flip effect disappears when party affiliation is observable on the ballot, which is consistent with the proposed causal mechanism.

stat.AP↗

arXiv2019

Logarithmic regret in the dynamic and stochastic knapsack problem with equal rewards

We study a dynamic and stochastic knapsack problem in which a decision maker is sequentially presented with items arriving according to a Bernoulli process over $n$ discrete time periods. Items have equal rewards and independent weights that are drawn from a known non-negative continuous distribution $F$. The decision maker seeks to maximize the expected total reward of the items that she includes in the knapsack while satisfying a capacity constraint and while making terminal decisions as soon as each item weight is revealed. Under mild regularity conditions on the weight distribution $F$, we prove that the regret---the expected difference between the performance of the best sequential algorithm and that of a prophet who sees all of the weights before making any decision---is, at most, logarithmic in $n$. Our proof is constructive. We devise a reoptimized heuristic that achieves this regret bound.

math.PR↗

arXiv2018

Uniformly bounded regret in the multi-secretary problem

In the secretary problem of Cayley (1875) and Moser (1956), $n$ non-negative, independent, random variables with common distribution are sequentially presented to a decision maker who decides when to stop and collect the most recent realization. The goal is to maximize the expected value of the collected element. In the $k$-choice variant, the decision maker is allowed to make $k \leq n$ selections to maximize the expected total value of the selected elements. Assuming that the values are drawn from a known distribution with finite support, we prove that the best regret---the expected gap between the optimal online policy and its offline counterpart in which all $n$ values are made visible at time $0$---is uniformly bounded in the the number of candidates $n$ and the budget $k$. Our proof is constructive: we develop an adaptive Budget-Ratio policy that achieves this performance. The policy selects or skips values depending on where the ratio of the residual budget to the remaining time stands relative to multiple thresholds that correspond to middle points of the distribution. We also prove that being adaptive is crucial: in general, the minimal regret among non-adaptive policies grows like the square root of $n$. The difference is the value of adaptiveness.

math.PR↗

arXiv2016

An adaptive $O(\log n)$-optimal policy for the online selection of a monotone subsequence from a random sample

Given a sequence of $n$ independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such a policy is within $O(\log n)$ of optimal. Our construction provides a direct and natural way for proving the $O(\log n)$-optimality gap. An earlier proof of the same result made crucial use of a key inequality of Bruss and Delbaen (2001) and of de-Poissonization.

math.PR↗

arXiv2016

A central limit theorem for costs in Bulinskaya's inventory management problem when deliveries face delays

It is common in inventory theory to consider policies that minimize the expected cost of ordering and holding goods or materials. Nevertheless, the realized cost is a random variable, and, as the Saint Petersburg Paradox reminds us, the expected value does not always capture the full economic reality of a decision problem. Here we take the classic inventory model of Bulinskaya (1964), and, by proving an appropriate central limit theorem, we show in a reasonably rich (and practical) sense that the mean-optimal policies are economically appropriate. The motivation and the tools are applicable to a large class of Markov decision problems.

math.PR↗

arXiv2015

A central limit theorem for temporally non-homogenous Markov chains with applications to dynamic programming

We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin (1956) for temporally non-homogeneous Markov chains, and the principal innovation is that here the summands are permitted to depend on both the current state and a bounded number of future states of the chain. We show through several examples that this added flexibility gives one a direct path to asymptotic normality of the optimal total reward of finite horizon Markov decision problems. The same examples also explain why such results are not easily obtained by alternative Markovian techniques such as enlargement of the state space.

math.PR↗

arXiv2015

Beardwood-Halton-Hammersley Theorem for Stationary Ergodic Sequences: a Counterexample

We construct a stationary ergodic process $X_1, X_2, \ldots $ such that each $X_t$ has the uniform distribution on the unit square and the length $L_n$ of the shortest path through the points $X_1, X_2, \ldots,X_n$ is not asymptotic to a constant times the square root of $n$. In other words, we show that the Beardwood, Halton and Hammersley theorem does not extend from the case of independent uniformly distributed random variables to the case of stationary ergodic sequences with uniform marginal distributions.

math.PR↗

arXiv2015

Quickest Online Selection of an Increasing Subsequence of Specified Size

Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a monotone increasing subsequence of a prespecified length $n$. This problem is dual to some online decision problems that have been considered earlier, and this dual problem has some notable advantages. In particular, the recursions and equations of optimality lead with relative ease to asymptotic formulas for mean and variance of the minimal selection time.

math.PR↗

arXiv2015

Optimal Online Selection of a Monotone Subsequence: a Central Limit Theorem

Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be accepted or rejected when it is first revealed. There is a unique selection policy $π_n^*$ that is optimal in the sense that it maximizes the expected value of $L_n(π_n^*)$, the number of selected observations. We investigate the distribution of $L_n(π_n^*)$; in particular, we obtain a central limit theorem for $L_n(π_n^*)$ and a detailed understanding of its mean and variance for large $n$. Our results and methods are complementary to the work of Bruss and Delbaen (2004) where an analogous central limit theorem is found for monotone increasing selections from a finite sequence with cardinality $N$ where $N$ is a Poisson random variable that is independent of the sequence.

math.PR↗

arXiv2013

Optimal On-Line Selection of an Alternating Subsequence: A Central Limit Theorem

We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of $n$ independent observations from a continuous distribution $F$, and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward recursion of dynamic programming and assembles a detailed understanding of the associated value functions and selection rules.

math.PR↗

arXiv2011

Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence

We consider the problem of selecting sequentially a unimodal subsequence from a sequence of independent identically distributed random variables, and we find that a person doing optimal sequential selection does within a factor of the square root of two as well as a prophet who knows all of the random observations in advance of any selections. Our analysis applies in fact to selections of subsequences that have d+1 monotone blocks, and, by including the case d=0, our analysis also covers monotone subsequences.

math.PR↗

arXiv2011

On-Line Selection of Alternating Subsequences from a Random Sample

We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12% worse than a person who can make selections with full knowledge of the random sequence.

math.PR↗