Group Choice with Interdependent Sublinear Voting

About the Project KAPSARC is developing the KAPSARC Toolkit for Behavioral Analysis (KTAB), an open source software platform, to support modeling and analysis of collective decision making processes (CDMPs). Within our research, KTAB is intended to be the standard platform for analyzing bargaining problems, generalized voting models and policy decision making. It is our intent to use KTAB to assemble the building blocks for a broad class of CDMPs. Typical models in KTAB will draw on the insights of subject matter experts regarding decision makers and influencers in a methodical, consistent manner and will then assist researchers to identify feasible outcomes that are the result of CDMPs.SummaryMany important decisions of policy are made in a collective manner, so a great deal of formal and informal analysis has been devoted to collective decision-making processes (CDMPs). One common approach to analyzing CDMPs is first to model the participants as exercising their ‘votes’ independently, and secondly to solve the model and identify a range of feasible outcomes. A potential criticism of this approach is that the actors may strategically modify their behaviors based on the behaviors of others. If such interdependent voting behaviors led to different outcomes, it would undermine the validity of analysis based on independent voting.In this paper, we compare and contrast two models of collective choice. The first assumes that each participant decides how much effort to exert as if they were acting alone; the second assumes that each participant strategically takes into account the effort exerted by other participants. While the first model is simpler, the second is more realistic.This paper demonstrates that they produce the same collective outcome: the simple model can be used without sacrificing realism. More formally, we demonstrate the mathematical equivalence of these two different CDMPs:The simple strategy of independent proportional voting, and some simple results of applying it.The consequences when actors strategically modify their behavior to take into account each other’s actions.There are some subtle differences in how the ‘negotiations’ play out — the actors do tend to exert less effort because of free rider effects — but overall the modified CDMP gives the same resultThus, we can analyze CDMPs as if the actors used independent proportional voting and remain confident that the final result is also correct should actors be using more strategically sophisticated behavior.

关于本项目，KAPSARC正在开发KAPSARC行为分析工具包（KTAB），这是一个开源的软件平台，旨在支持集体决策过程（CDMPs）的建模与分析。在我们的研究中，KTAB旨在成为分析谈判问题、广义投票模型和政策决策的标准平台。我们的意图是利用KTAB构建一类广泛的CDMPs的基本模块。KTAB中的典型模型将按照系统性和一致性的方式，借鉴领域专家关于决策者和影响者的见解，并协助研究者识别CDMPs产生的可行结果。总结而言，许多政策的重要决策是通过集体方式作出的，因此，大量正式和非正式的分析都致力于集体决策过程（CDMPs）。分析CDMPs的一种常见方法是将参与者视为独立行使‘投票权’，其次解决模型并识别一系列可行结果。这种方法的潜在批评是，行为者可能会根据他人的行为策略性地调整自己的行为。如果这种相互依赖的投票行为导致不同的结果，将削弱基于独立投票的分析的有效性。在本论文中，我们对比分析了两种集体选择的模型。第一种假设每个参与者决定投入多少努力，仿佛他们是在独立行动；第二种假设每个参与者策略性地考虑到其他参与者所付出的努力。虽然第一种模型较为简单，但第二种模型更为现实。本文证明了它们产生相同的集体结果：简单模型可以在不牺牲现实性的情况下使用。更正式地说，我们证明了这两种不同的CDMPs在数学上的等价性：独立的成比例投票的简单策略，以及应用该策略的一些简单结果。当行为者策略性地调整自己的行为以考虑彼此的行动时，产生的后果。在‘谈判’的展开过程中存在一些微妙的不同——由于搭便车效应，行为者往往会付出较少的努力——但总体而言，修改后的CDMP给出相同的结果。因此，我们可以将CDMPs视为行为者使用独立的成比例投票进行分析，并保持信心，即使行为者使用更为策略和复杂的行为，最终结果也将是正确的。