Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than single votes. In practice, elections using IRV often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k-1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide a construction matching the lower bound for unrestricted voter preferences. Additionally, we characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. We also examine how classic preference restrictions influence our results—for instance, single-peakedness makes k-1 different winners impossible but still allows at least Ω(√k). Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.
more »
« less
Modeling Voters in Multi-Winner Approval Voting
In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-k candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in single-winner and multi-winner approval voting scenarios with varying degrees of uncertainty using behavioral data obtained from Mechanical Turk. We find that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. There are a number of predictive models of agent behavior in the social choice and psychology literature that are based on cognitively plausible heuristic strategies. We show that the existing approaches do not adequately model our real-world data. We propose a novel model that takes into account the size of the winning set and human cognitive constraints; and demonstrate that this model is more effective at capturing real-world behaviors in multi-winner approval voting scenarios.
more »
« less
- Award ID(s):
- 2007955
- NSF-PAR ID:
- 10309913
- Date Published:
- Journal Name:
- Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
It remains an open question how to determine the winner of an election given incomplete or uncertain voter preferences. One solution is to assume some probability space for the voting profile and declare that the candidates having the best chance of winning are the (co-)winners. We refer to this interpretation as the Most Probable Winner (MPW). In this paper, we focus on elections that use positional scoring rules, and propose an alternative winner interpretation, the Most Expected Winner (MEW), according to the expected performance of the candidates. We separate the uncertainty in voter preferences into the generation step and the observation step, which gives rise to a unified voting profile combining both incomplete and probabilistic voting profiles. We use this framework to establish the theoretical hardness of MEW over incomplete voter preferences, and then identify a collection of tractable cases for a variety of voting profiles, including those based on the popular Repeated Insertion Model (RIM) and its special case, the Mallows model. We develop solvers customized for various voter preference types to quantify the candidate performance for the individual voters, and propose a pruning strategy that optimizes computation. The performance of the proposed solvers and pruning strategy is evaluated extensively on real and synthetic benchmarks, showing that our methods are practical.more » « less
-
Relevance to proposal: This project evaluates the generalizability of real and synthetic training datasets which can be used to train model-free techniques for multi-agent applications. We evaluate different methods of generating training corpora and machine learning techniques including Behavior Cloning and Generative Adversarial Imitation Learning. Our results indicate that the utility-guided selection of representative scenarios to generate synthetic data can have significant improvements on model performance. Paper abstract: Crowd simulation, the study of the movement of multiple agents in complex environments, presents a unique application domain for machine learning. One challenge in crowd simulation is to imitate the movement of expert agents in highly dense crowds. An imitation model could substitute an expert agent if the model behaves as good as the expert. This will bring many exciting applications. However, we believe no prior studies have considered the critical question of how training data and training methods affect imitators when these models are applied to novel scenarios. In this work, a general imitation model is represented by applying either the Behavior Cloning (BC) training method or a more sophisticated Generative Adversarial Imitation Learning (GAIL) method, on three typical types of data domains: standard benchmarks for evaluating crowd models, random sampling of state-action pairs, and egocentric scenarios that capture local interactions. Simulated results suggest that (i) simpler training methods are overall better than more complex training methods, (ii) training samples with diverse agent-agent and agent-obstacle interactions are beneficial for reducing collisions when the trained models are applied to new scenarios. We additionally evaluated our models in their ability to imitate real world crowd trajectories observed from surveillance videos. Our findings indicate that models trained on representative scenarios generalize to new, unseen situations observed in real human crowds.more » « less
-
null (Ed.)How cells with different genetic makeups compete in tissues is an outstanding question in developmental biology and cancer research. Studies in recent years have revealed that cell competition can either be driven by short-range biochemical signalling or by long-range mechanical stresses in the tissue. To date, cell competition has generally been characterised at the population scale, leaving the single-cell-level mechanisms of competition elusive. Here, we use high time-resolution experimental data to construct a multi-scale agent-based model for epithelial cell competition and use it to gain a conceptual understanding of the cellular factors that governs competition in cell populations within tissues. We find that a key determinant of mechanical competition is the difference in homeostatic density between winners and losers, while differences in growth rates and tissue organisation do not affect competition end result. In contrast, the outcome and kinetics of biochemical competition is strongly influenced by local tissue organisation. Indeed, when loser cells are homogenously mixed with winners at the onset of competition, they are eradicated; however, when they are spatially separated, winner and loser cells coexist for long times. These findings suggest distinct biophysical origins for mechanical and biochemical modes of cell competition.more » « less
-
In multi-agent domains (MADs), an agent's action may not just change the world and the agent's knowledge and beliefs about the world, but also may change other agents' knowledge and beliefs about the world and their knowledge and beliefs about other agents' knowledge and beliefs about the world. The goals of an agent in a multi-agent world may involve manipulating the knowledge and beliefs of other agents' and again, not just their knowledge/belief about the world, but also their knowledge about other agents' knowledge about the world. Our goal is to present an action language (mA+) that has the necessary features to address the above aspects in representing and RAC in MADs. mA+ allows the representation of and reasoning about different types of actions that an agent can perform in a domain where many other agents might be present -- such as world-altering actions, sensing actions, and announcement/communication actions. It also allows the specification of agents' dynamic awareness of action occurrences which has future implications on what agents' know about the world and other agents' knowledge about the world. mA+ considers three different types of awareness: full-, partial- awareness, and complete oblivion of an action occurrence and its effects. This keeps the language simple, yet powerful enough to address a large variety of knowledge manipulation scenarios in MADs. The semantics of mA+ relies on the notion of state, which is described by a pointed Kripke model and is used to encode the agent's knowledge and the real state of the world. It is defined by a transition function that maps pairs of actions and states into sets of states. We illustrate properties of the action theories, including properties that guarantee finiteness of the set of initial states and their practical implementability. Finally, we relate mA+ to other related formalisms that contribute to RAC in MADs.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
