15 research outputs found
Migration as Submodular Optimization
Migration presents sweeping societal challenges that have recently attracted
significant attention from the scientific community. One of the prominent
approaches that have been suggested employs optimization and machine learning
to match migrants to localities in a way that maximizes the expected number of
migrants who find employment. However, it relies on a strong additivity
assumption that, we argue, does not hold in practice, due to competition
effects; we propose to enhance the data-driven approach by explicitly
optimizing for these effects. Specifically, we cast our problem as the
maximization of an approximately submodular function subject to matroid
constraints, and prove that the worst-case guarantees given by the classic
greedy algorithm extend to this setting. We then present three different models
for competition effects, and show that they all give rise to submodular
objectives. Finally, we demonstrate via simulations that our approach leads to
significant gains across the board.Comment: Simulation code is available at https://github.com/pgoelz/migration
Approval-Based Apportionment
In the apportionment problem, a fixed number of seats must be distributed
among parties in proportion to the number of voters supporting each party. We
study a generalization of this setting, in which voters cast approval ballots
over parties, such that each voter can support multiple parties. This
approval-based apportionment setting generalizes traditional apportionment and
is a natural restriction of approval-based multiwinner elections, where
approval ballots range over individual candidates. Using techniques from both
apportionment and multiwinner elections, we are able to provide representation
guarantees that are currently out of reach in the general setting of
multiwinner elections: First, we show that core-stable committees are
guaranteed to exist and can be found in polynomial time. Second, we demonstrate
that extended justified representation is compatible with committee
monotonicity
Generative Social Choice
Traditionally, social choice theory has only been applicable to choices among
a few predetermined alternatives but not to more complex decisions such as
collectively selecting a textual statement. We introduce generative social
choice, a framework that combines the mathematical rigor of social choice
theory with large language models' capability to generate text and extrapolate
preferences. This framework divides the design of AI-augmented democratic
processes into two components: first, proving that the process satisfies
rigorous representation guarantees when given access to oracle queries; second,
empirically validating that these queries can be approximately implemented
using a large language model. We illustrate this framework by applying it to
the problem of generating a slate of statements that is representative of
opinions expressed as free-form text, for instance in an online deliberative
process
Approval-based apportionment
In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters can support multiple parties by casting approval ballots. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates instead of parties. Using techniques from both apportionment and multiwinner elections, we identify rules that generalize the D’Hondt apportionment method and that satisfy strong axioms which are generalizations of properties commonly studied in the apportionment literature. In fact, the rules we discuss provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we show that core-stable committees are guaranteed to exist and can be found in polynomial time. Second, we demonstrate that extended justified representation is compatible with committee monotonicity (also known as house monotonicity)
Envy-Free and Pareto-Optimal Allocations for Agents with Asymmetric Random Valuations
We study the problem of allocating indivisible items to agents with
additive utilities. It is desirable for the allocation to be both fair and
efficient, which we formalize through the notions of envy-freeness and
Pareto-optimality. While envy-free and Pareto-optimal allocations may not exist
for arbitrary utility profiles, previous work has shown that such allocations
exist with high probability assuming that all agents' values for all items are
independently drawn from a common distribution. In this paper, we consider a
generalization of this model where each agent's utilities are drawn
independently from a distribution specific to the agent. We show that envy-free
and Pareto-optimal allocations are likely to exist in this asymmetric model
when , which is tight up to a log log gap that
also remains open in the symmetric subsetting. Furthermore, these guarantees
can be achieved by a polynomial-time algorithm.Comment: Appeared in IJCAI 22
Synthesis in Distributed Environments
Most approaches to the synthesis of reactive systems study the problem in
terms of a two-player game with complete observation. In many applications,
however, the system's environment consists of several distinct entities, and
the system must actively communicate with these entities in order to obtain
information available in the environment. In this paper, we model such
environments as a team of players and keep track of the information known to
each individual player. This allows us to synthesize programs that interact
with a distributed environment and leverage multiple interacting sources of
information.
The synthesis problem in distributed environments corresponds to solving a
special class of Petri games, i.e., multi-player games played over Petri nets,
where the net has a distinguished token representing the system and an
arbitrary number of tokens representing the environment. While, in general,
even the decidability of Petri games is an open question, we show that the
synthesis problem in distributed environments can be solved in polynomial time
for nets with up to two environment tokens. For an arbitrary but fixed number
of three or more environment tokens, the problem is NP-complete. If the number
of environment tokens grows with the size of the net, the problem is
EXPTIME-complete.Comment: 12 pages excluding references and appendices, 29 pages total, 5
figures. Version without appendices to be published in conference proceedings
of FSTTCS 2017. Appendix A includes notation for multisets. Appendix B
includes detailed proofs that have been omitted due to space constraints.
Appendix C contains an algorithm for symbolic evaluation of commitments and
its runtime analysi
Approval-Based Apportionment
In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters cast approval ballots over parties, such that each voter can support multiple parties. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates. Using techniques from both apportionment and multiwinner elections, we are able to provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we show that core-stable committees are guaranteed to exist and can be found in polynomial time. Second, we demonstrate that extended justified representation is compatible with committee monotonicity
Dynamic Placement in Refugee Resettlement
Employment outcomes of resettled refugees depend strongly on where they are
placed inside the host country. Each week, a resettlement agency is assigned a
batch of refugees by the United States government. The agency must place these
refugees in its local affiliates, while respecting the affiliates' yearly
capacities. We develop an allocation system that suggests where to place an
incoming refugee, in order to improve total employment success. Our algorithm
is based on two-stage stochastic programming and achieves over 98 percent of
the hindsight-optimal employment, compared to under 90 percent of current
greedy-like approaches. This dramatic improvement persists even when we
incorporate a vast array of practical features of the refugee resettlement
process including indivisible families, batching, and uncertainty with respect
to the number of future arrivals. Our algorithm is now part of the Annie MOORE
optimization software used by a leading American refugee resettlement agency.Comment: Expanded related work, added experiments with bootstrapped arrivals
in Section 7.2, added various experiments in the appendi