Generalisation of Samet's (2010) agreement theorem

We develop a framework that allows us to reproduce the generalised agreement theorem of Samet (2010), and extend it to models with a non-partitional information structure, while highlighting the features that distinguish the result from the classic theorems found in the literature. Furthermore, we produce results that are similar to Samet’s with some modified assumptions

Social network markets: the influence of network structure when consumers face decisions over many similar choices

In social network markets, the act of consumer choice in these industries is governed not just by the set of incentives described by conventional consumer demand theory, but by the choices of others in which an individual's payoff is an explicit function of the actions of others. We observe two key empirical features of outcomes in social networked markets. First, a highly right-skewed, non-Gaussian distribution of the number of times competing alternatives are selected at a point in time. Second, there is turnover in the rankings of popularity over time. We show here that such outcomes can arise either when there is no alternative which exhibits inherent superiority in its attributes, or when agents find it very difficult to discern any differences in quality amongst the alternatives which are available so that it is as if no superiority exists. These features appear to obtain, as a reasonable approximation, in many social network markets. We examine the impact of network structure on both the rank-size distribution of choices at a point in time, and on the life spans of the most popular choices. We show that a key influence on outcomes is the extent to which the network follows a hierarchical structure. It is the social network properties of the markets, the meso-level structure, which determine outcomes rather than the objective attributes of the products.Comment: 14 pages, 5 figure

Agreeing to disagree: a syntactic approach

We develop a syntactic framework that allows us to emulate standard results from the “agreeing to disagree” literature with generalised decision functions (e.g. Bacharach (1985)) in a manner the avoids known incoherences pointed out by Moses and Nachum (1990). Avoiding the incoherences requires making some sacrifices: For example, we must require the decision functions to be independent of interactive information, and, the language in which the states are described must be “rich” - in some well-defined sense. Using weak additional assumptions, we also extend all previous results to allow agents to base their decisions on possibly false information. Finally, we provide agreement theorems in which the decision functions are not required to satisfy the Sure-Thing Principle (a central assumption in the standard results)

Generalisation of Samet's (2010) agreement theorem

We develop a framework that allows us to reproduce the generalised agreement theorem of Samet (2010), and extend it to models in which agents can base their decisions on false information, while highlighting the features that distinguish the result from the classic theorems found in the literature. For example, it allows decisions to be based on interactive information, and imposes no requirements on the language in which the states are described. Finally, we produce a result that does not require Samet’s assumption of the existence of a completely uninformed agent

Generalisation of Samet's (2010) agreement theorem

We develop a framework that allows us to reproduce the generalised agreement theorem of Samet (2010), and extend it to models in which agents can base their decisions on false information, while highlighting the features that distinguish the result from the classic theorems found in the literature. For example, it allows decisions to be based on interactive information, and imposes no requirements on the language in which the states are described. Finally, we produce results that are similar to Samet’s but that do not require his assumption of the existence of a completely uninformed agent

Agreeing to disagree: a syntactic approach

We develop a syntactic framework that allows us to emulate standard results from the “agreeing to disagree” literature with generalised decision functions (e.g. Bacharach (1985)) in a manner the avoids known incoherences pointed out by Moses and Nachum (1990). Avoiding the incoherences requires making some sacrifices: For example, we must require the decision functions to be independent of interactive information, and, the language in which the states are described must be “rich” - in some well-defined sense. Using weak additional assumptions, we also extend all previous results to allow agents to base their decisions on possibly false information. Finally, we provide agreement theorems in which the decision functions are not required to satisfy the Sure-Thing Principle (a central assumption in the standard results)

Agreeing to disagree with generalised decision functions

We develop a framework that allows us to emulate standard results from the “agreeing to disagree" literature with generalised decision functions (e.g. Bacharach (1985)) in a manner the avoids known incoherences pointed out by Moses and Nachum (1990). We analyse the implications of the Sure-Thing Principle, a central assumption. The upshot is that the way in which states are described matters, and that the results fail if decisions are allowed to depend on interactive information. Furthermore, using very weak additional assumptions, we extend all previous results to models with a non-partitional information structure in a coherent manner. Finally, we provide agreement theorems in which the decision functions are not required to satisfy the Sure-Thing Principle

Generalisation of Samet's (2010) agreement theorem

We develop a framework that allows us to reproduce the generalised agreement theorem of Samet (2010), and extend it to models in which agents can base their decisions on false information, while highlighting the features that distinguish the result from the classic theorems found in the literature. For example, it allows decisions to be based on interactive information, and imposes no requirements on the language in which the states are described. Finally, we produce results that are similar to Samet’s but that do not require his assumption of the existence of a completely uninformed agent

Agreement theorems with interactive information: possibilities and impossibilities

Following from Tarbush (2011a), we explore the implications of using two different definitions of informativeness over kens; one that ranks objective, and the other subjective information. With the first, we create a new semantic operation that allows us to derive agreement theorems even when decision functions are based on interactive information (for any r ≥ 0). Effectively, this operation, unlike information cell union captures the notion of an agent becoming “more ignorant” for all modal depths. Using the definition that ranks subjective information however, we show an impossibility result: In generic models, agreement theorems using the standard Sure-Thing Principle do not hold when decision functions depend on interactive information (when r > 0)