• Start Date: September 21, 2021
  • End Date: September 22, 2021
  • Event Start Time: 9:00 AM
  • Event End Time: 9:00 AM
  • Organizers: Ashish Goel
  • Social choice has a rich history tracing back to the work of Borda, Condorcet, Laplace and others in the 18th century, and the work of Kenneth Arrow in the 1950s that led to the Nobel Prize in Economics. A current working definition might say that social choice theory studies how to aggregate individual preferences toward making a collective choice.

    Beginning in the late 1980s social choice theory touched theoretical computer science, and questions arose about the computational difficulty of calculating the winner of an election or of manipulating the outcome through strategic voting. The field of computational or algorithmic social choice has exploded since then. In this workshop, we explore some of the key new directions of research, emphasizing two directions: (1) developing new algorithmic methods for analyzing social choice rules/mechanisms and constructing new ones; and (2) applying concepts of social choice to issues of interest in modern computer science, such as crowdsourcing, group recommender systems, and information retrieval systems. As Brandt, et al (2016) observe, today there is “increasing awareness of the great potential of computational social choice for important applications of decision-making technologies, in areas as diverse as policy making (e.g., matching junior doctors to hospitals), distributed computing (e.g., allocating bandwidth to processes), and education (e.g., aggregating student evaluations gathered by mean of peer assessment methods).”

    The workshop will explore new concepts of design of auctions, voting rules, or matching mechanisms that perform well when the individual “voters” are behaving strategically – an old topic with new twists (Nisan, 2007). Here we will study such topics as “approximate mechanism design without money” (Procaccia and Tennenholtz, 2013) and “incentive compatible machine learning” (Dekel, et al, 2010).

    One focus will be methods to scale up collaboration and decision making, enabling large communities to deliberate and brainstorm with one another on important issues with the aid of intelligently designed algorithms and digital communication platforms. The goal is to design tools that not only aid decision-makers in harnessing collective intelligence, but also create community members who are more informed and engaged in making their communities better. An example is the Stanford Participatory Budgeting Platform that allows cities, municipalities, states, foundations, and other organizations to offer a form of direct democracy where members vote to determine how the budget is allocated. Recent new algorithms for participatory budgeting show promise (Goel et al., 2019; Freeman et al., 2019).

    Another theme will be randomized social choice. We will study preferences over probability distributions and in particular issues of strategyproofness in this context (Aziz, Brandt, and Brill, 2013b, Aziz, Brandl, and Brill, 2014); randomization in social choice (Kavitha, Mestre, and Nasre, 2011, Aziz, Brandt, and Stursberg, 2013); and concepts of random serial dictators (Aziz, Brandt, and Brill, 2013a, Aziz and Mestre 2014).

    The workshop will also explore iterative voting, where voters cast votes in rounds, observing the outcomes of earlier rounds. An old topic in this area has to do with the Delphi method developed at the RAND Corporation in the 1960s (see, e.g, Dalkey, 1969). Here we study questions such as: For what voting rules and iterative voting models does the process converge? When does it converge to an outcome with desirable properties? For instance, Meir, et al. (2010) studied this problem for the plurality rule and showed that under some process assumptions the process converges to a Nash equilibrium; and Airiau and Endriss (2009) study the process where at each step a voter is randomly selected to propose a new alternative to the current winner. Other questions are: what can be concluded if voters have incomplete knowledge of others’ voting intentions (Reijngoud and Endriss, 2012), or if there is uncertainty in information about knowledge of others’ intentions (Meir, Lev, and Rosenschein, 2014).

  • Monday, September 20, 2021

    Workshop Talks

    9:00 AM – 9:30 AM

    Organizers Welcome

    9:30 AM – 10:30 AM

    Faster Tree Edit Distance via APSP Equivalence

    Jakob Nogler - Massachusetts Institute of Technology

    The Tree Edit Distance (TED) between two rooted, ordered trees with n nodes labeled from an alphabet Σ is defined as the minimum cost to transform one tree into the other via a sequence of valid node insertions, deletions, and relabelings. First introduced by Selkow in the late 1970s, the algorithmic computation of TED has seen numerous improvements over the decades, culminating in an O(n³)-time algorithm [DMRW 2010]. In this presentation, we sketch the proof from our recent STOC 2025 paper showing that TED is fine-grained equivalent to the All-Pairs Shortest Path (APSP) problem. Our reduction is tight enough that, combined with the fastest APSP algorithm [Williams 2018], it yields the first slightly subcubic algorithm for TED, running in n³ / 2^(Ω(√(log n))) time. We also extend the proof to unweighted TED, where each edit costs one. Here, we achieve a runtime of O(n^((3+ω)/2)), matching the bound for the monotone min-plus product and closing the gap left by previous algorithms [Mao 2022, Dürr 2023] that incurred losses in their exponents.

    10:30 AM – 11:30 AM

    Frontier Space-Time Algorithms Using Only Full Memory

    Michal Koucký - Charles University

    We develop catalytic algorithms for fundamental problems in algorithm design that run in polynomial time, use only $O(log(n))$ workspace, and use sublinear catalytic space matching the best-known space bounds of non-catalytic algorithms running in polynomial time.

    First, we design a polynomial time algorithm for directed $s$-$t$ connectivity using $n big/ 2^{Theta(sqrt{log n})}$ catalytic space, which matches the state-of-the-art time-space bounds in the non-catalytic setting [Barnes et al., 1998],, and improves the catalytic space usage of the best known algorithm [Cook and Pyne, 2026]. Furthermore, using only $O(log(n))$ random bits we get a randomized algorithm whose running time nearly matches the fastest time bounds known for space-unrestricted algorithms.

    Second, we design polynomial time algorithms for the problems of computing Edit Distance, Longest Common Subsequence, and the Discrete Frechet Distance, again using $n big/ 2^{Theta(sqrt{log n})}$ catalytic space. This again matches non-catalytic time-space frontier for Edit Distance and Least Common Subsequence [Kiyomi et al., 2021].

    11:30 AM – 12:30 PM

    The Forbidden Structure Method in Graph Metric Sparsification

    Greg Bodwin - University of Michigan

    We will survey the "forbidden structure method," a recently-popular technique for building graph metric sparsifiers. In this method, one uses a simple greedy algorithm to construct a sparsifier, and then shows that the resulting sparsifier does not contain a certain substructure. Then, one applies bounds from extremal combinatorics to control the maximum possible size of a graph avoiding this structure. We will demonstrate this method on spanners, preservers, shortcut sets, and hopsets as our main sparsifiers of interest.

    12:30 PM – 2:00 PM

    Lunch (on your own)

    2:00 PM – 3:00 PM

    Universe Reduction for APSP: Equivalence of Three Fine-Grained Hypotheses

    Nick Fischer - Max Planck Institute for Informatics

    The All-Pairs Shortest Paths (APSP) problem is to compute all pairs of distances in a given weighted graph, and the associated *APSP Hypothesis* states that the APSP cannot be solved in subcubic time. Two increasingly stronger assumptions are the *Strong APSP Hypothesis* and the *Directed Unweighted APSP Hypothesis* which state that the fastest-known APSP algorithms on graphs with small weights and unweighted graphs, respectively, are best-possible. In this talk we discuss a surprising connection between these three regimes (unweighted, small weights, polynomially bounded weights): There is an efficient universe reduction for APSP, implying that the three hypotheses are actually equivalent, conditioned on $omega = 2$ and a plausible additive combinatorics assumption. The proof technique is centered around novel rank measure, called the *select-plus rank* of a matrix, and leads to many interesting other results, including some long-awaited APSP-based lower bounds. (Based on this paper: https://arxiv.org/abs/2603.27736)

  • Audiences: General Research