Public Good Indices for Games with Several Levels of Approval

This work focuses on (j, 2) games in which there are several levels of approval in the input, i. e. games with n players, j ordered qualitative alternatives in the input level and 2 possible ordered quantitative alternatives in the output. When considering (j, 2) games, we extend the Public Good index (PGI), the Null Player Free index (NPFI) and the Shift index (SI) and provide full characterizations of these extensions.

Voting Power and the Public Good Index: Some Thoughts

Among the many voting power indices, the public good index (PGI) is one of the less well-known ones. Holler (2018) posits some hypotheses about why this is the case. In response, I share a few thoughts here on voting power in general and about the popularity of the PGI.

Power, Outcomes and Preferences / Macht, Ereignisse und Präferenzen

SummaryThere is an ongoing discussion about the relationship of power and preferences: Is power reflected in what the agents can do and what they want to do, or, alternatively, are preferences and power two separate dimensions of determining the outcome of decisionmaking? In the latter case decisionmaking is troubled with all kinds of paradoxes which do not allow to derive well-defined outcomes which can relate preferences to resources (votes), decision rules, and power – if we do not subscribe to the rather rigorous assumption of single-peaked preferences on a one-dimensional preference space. This paper raises the question whether these paradoxes do not undermine a power concept which combines preferences and collective decision rules, described by games, with resulting outcomes. A discussion of the Public Good Index with respect to decision rules concludes the paper.