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.

Summary

Many 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 result

Thus, 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.