Social interaction, knowledge, and social software

Abstract

In [31] a theory of human computation, analogous to Turing's theory of machine computation, is discussed. The issue there is whether there might be an analogue to Church's thesis in this human domain. Examples of human algorithms discussed include the making of scrambled eggs. By comparison, Lynn Stein in this volume discusses the making of a peanut butter and jelly sandwich. Neither she nor us in this volume have any concern with Church's thesis as such, although that might prove to be a fascinating topic for a future paper. Rather the issue here is interaction, which occurs most naturally in multiagent algorithms, unlike the making of scrambled eggs or peanut butter sandwiches where one agent normally suffices.1 Such multiagent algorithms, examples of which are building a house, or playing bridge, are examples of what we shall call social software after [32]. In that paper, one of us asked "Is it possible to create a theory of how social procedures work with a view to creating better ones and ensuring the c rrectness of the ones we do have?" The present chapter will survey some of the logical and mathematical tools that have been developed over the years that may help address this question. Social procedures occur at two levels. One is the purely personal level where an individual is able to perform some complex action because social structures have been set up to enable such an action. Taking a train (which requires a system) or even a bath (where the city must supply not only the water but also a system of pipes to carry it) are examples of such situations where an individual is doing something simple or complex which is enabled by existing social structures. Procedures which are truly social are those which require more than one individual even in their execution. A piano duet is a simple example, but holding an election or passing a bill through the Senate are more complex ones. Computer programs, whether sequential or distributed, have logical and algorithmic properties which can be analyzed by means of appropriate logics of programs. Similarly, these social procedures also have logical properties which can be analyzed by means of the appropriate logical tools, augmented by tools from game theory, perhaps even from psychology. There are several ways to compare social software with distributed computing. In both cases the issue of knowledge arises. When several processes, whether human or computer, are taking part in a common procedure, then they need to know enough of what others are doing so as to be able to do their part when the time comes. Indeed, Halpern and Moses' fundamental paper on common knowledge was written in the context of distributed computing, although other authors like Aumann (game theory, see [2, 3]) and Lewis (social agreement, see [17] ) had a different setting. Thus knowledge matters and we shall give a quick survey of current formal theories of knowledge. However, unless the agents have the same goal, or at least compatible goals, there may be some element of strategizing where each agent ries to maximize its own benefit (sometimes represented as utility ) while keeping in mind what other agents are apt to do. This makes game theory relevant. In the context of social programming where an overarching social agent (say, a government) is trying to make agents act in a socially beneficial way, the social agent will still need to take into account the fact that while its own goal is social welfare, the goal of the individual agent is his own personal welfare. Thus agents have to be guided to act in beneficial ways. A simple example of this is the system of library fines to ensure that borrowers do not keep books too long and prevent other borrowers from having access to them. Finally, agents may sometimes act in concert with other agents, i.e., form coalitions. There is an extensive theory of co-operative games but our primary purpose here will be to give a brief account of the logical theory of coalitions due to Marc Pauly. Thus what we hope to do in this chapter is to survey some of these logica and analytical tools and indicate a few applications. These tools are: 1. Logic of knowledge 2. Logic of games 3. Game theory and economic design In the following sections we shall give brief descriptions of these three tools and then indicate some applications. We assume that the reader has some mild acquaintance with game theory (although we shall not actually use very much), and [16] is a good reference for that field. Moore [18] gives a survey of economic design. The sections are reasonably independent and the applications depend mainly on reasoning about knowledge. © 2006 Springer-Verlag Berlin Heidelberg.