An Electoral Approach to Diversify LLM -based Multi-Agent Collective Decision-Making (2024)

Abstract: Modern large language models (LLMs) have exhibited cooperative synergy on complex task-solving, and collective decision-making (CDM) is a pivotal component in LLM-based multi-agent collaboration frameworks. Our survey on 52 recent such systems uncovers a severe lack of diversity, with a heavy reliance on dictatorial and plurality voting for CDM. Through the lens of social choice theory, we scrutinize widely-adopted CDM methods and identify their limitations. To enrich current landscape of LLM-based CDM, we present GEDI, an electoral CDM module that incorporates various ordinal preferential voting mechanisms. Our empirical case study across three benchmarks shows that the integration of certain CDM methods can markedly improve the reasoning capabilities and robustness of some leading LLMs, all without requiring intricate system designs. Additionally, we find that some CDM mechanisms generate positive synergies even with as few as three agents. The voting-based methods also demonstrate robustness against single points of failure, as well as diversity in terms of hit-rate@k and subject-wise impacts.

## introduction while multi-agent systems have constantly garnered attention even before the advent of large language models (llms), as evidenced by prior works @xcite . the recent advancements in llms have significantly sparked interest in llm-based agents. furthermore, novel techniques such as effective prompt engineering @xcite and agentinteraction schemes @xcite have propelled a surge in research on collaborative llm agents @xcite . researchers have deployed llm-based agents in various environments and scenarios: from 23 13 1 15 dictatorial plurality utilitarian unspecified simulating small community @xcite to predicting court judgement @xcite , crafting digital avatars @xcite , and participating in dialogue-based games @xcite @xcite , among others. however, the existing accounts on llm-based multi-agent collaboration has been heavily focusing on inter-agent communication and interaction workflows. in contrast, another vital aspect, collective decision-making (cdm), appears to have been largely neglected and overly simplified. our review of 52 recent llm collaboration systems ( § 2) reveals that systems either appoint a 'dictator' agent to make decisions for the group @xcite or depend on simplistic plurality voting @xcite @xcite , with one case adopting an utilitarian approach @xcite . this study examines prevalent cdm methods through the lens of social choice theory @xcite and illustrate their failure to meet fundamental criteria ( § 3): dictatorial methods are fragile for their absolute dependency on one single agent; plurality voting, while simple and intuitively flawless, disqualifies independence from irrelevant alternatives (iia) and condorcet criterion; utilitarian violates both majority and condorcet criteria. such deviations from key criteria may impede the transition from individual preferences to collective decisions among llm-based agents. while arrow's theorems @xcite establishes the axiomatic impossibility of designing a perfect voting-based cdm system, we can still circumvent some limitations and risks by incorporating a variety of cdm methods into llm-based multi-agent frameworks. to this end, we develop an electoral cdm module, gedi ( § 4), which offers a range of cdm mechanisms that were not previously tested in such frameworks. to evaluate the potential impact of various cdm methods, we conduct an empirical case study ( § 5) on three multiplechoice question-answering (mcqa) benchmarks: mmlu @xcite , @xcite , and arc-challenge @xcite , using a suite of models with various sizes and architectures. our key findings ( § 5.2) are as follows: (1) applying a cdm method generally leads to better results compared to a single-agent decision-making on mcqa benchmarks, though at the cost of increased computation; (2) the degree of synergy depends significantly on the backbone model and the benchmark. some llms exhibit substantial improvements with voting-based methods, while others show little to no effect under any cdm; we hope these observations will encourage further evaluation of the effectiveness of llm-based multi-agent frameworks and provide valuable insights for advancing llm-based multi-agent systems (mas). ## a social choice theory perspective on collective decision-making social choice theory concerns passing from individual preferences to collective decisions @xcite . while humans have practiced and refined collective decision-making since antiquity, modern social choice theory has not been established until the publishing of kenneth j. arrow's renowned social choice and individual values @xcite , which axiomatically formalizes the theory and comparatively analyzes various electoral systems. ## diversifying llm-based multi-agent cdm to enhance the diversity of cdm approaches within llm-agent frameworks, we propose incorporating a range of cdm methods rooted in human socio-political practices. specifically, we craft an electoral cdm module, named general electoral decision-making interface (gedi), which integrates several common ordinal preferential voting systems. figure 2 highlights a few key distinctions between gedi and other commonly used cdm methods in llm-based mas. ## conclusion and future work in the midst of the expanding research on llmbased agents, we have surveyed 52 multi-agent collaboration frameworks and revealed a significant lack of diversity in cdm. we have scrutinized popular cdm methods and indicate their fundamental limitations through a social choice theory perspective. aiming to diversify the current cdm landscape, we have drew inspiration from human societal practices and explored various cdm methods in an empirical case study across multiple benchmarks. our experiments have produced a wealth of observations and insights, demonstrating how such diversification can illuminate the study of collective behaviors in llms. our study also opens up numerous avenues for future research. for instance, matching specific tasks with appropriate cdm methods to enhance agent decision-making quality holds promising practical value. moreover, since social choice theory addresses collective preferences, we expect that it could inspire broader interdisciplinary nlp research, particularly language model alignment and aggregation.