**Analyzing Probabilistic Specifications with Supercomputers**

Our analyses of the probabilistic specifications of choice models are computationally intensive. As a result we require supercomputing resources. For instance, some of our studies might require 50,000 or more service units (SU), where a SU is defined as one hour of computation time on one core of a supercomputing cluster. Supercomputing clusters have thousands of cores. Common desktop computers might have 2, 3 or 4 cores.

We have our supercomputing allocation through the National Science Foundation’s ** Extreme Science and Engineering Discovery Environment**, or XSEDE. XSEDE is a consortium of supercomputing clusters in the U.S. Currently we run our analyses on Blacklight at the **Pittsburgh Supercomputing Center**. Blacklight is one of the few clusters in XSEDE that has Matlab. And some parts of our analyses require Matlab.

**Individual Intertemporal Choice**

Intertemporal choices underlie many of society’s most pressing decisions, from collective decisions such as global climate change and the war on obesity to more personal decisions such as consuming alcohol and investing in retirement plans. Virtually all decisions we make have a temporal component. This makes intertemporal choice relevant across a broad range of disciplines (e.g., economics, psychology, biology, neuroscience, finance, medicine, environmental science). Despite the extensive interest in this topic, there still is a critical gap in our knowledge of how individuals make intertemporal choices.

Imagine binary choice data on intertemporal choice behavior. Suppose that, for each pair of prospects, the modal (most frequent) choice among participants is the choice predicted by Exponential Discounting, a leading theory. Imagine that the modal choice of not even one single pair of prospects is consistent with Hyperbolic Discounting, a leading competitor to Exponential Discounting. Would this provide overwhelming evidence for Exponential over Hyperbolic Discounting? Actually, it is possible in such an experiment that every individual participant made choices in violation of Exponential and consistent with Hyperbolic Discounting! Aggregated data can be extremely misleading as to the underlying decision process, because of aggregation paradoxes similar to the famous voting paradoxes of social choice theory. This problem eludes much of the research community because individual and social choice researchers rarely collaborate.

A second, and equally important problem is that much behavioral research on decision making relies on overly rudimentary mathematical and statistical methods for testing theories. A number of scholars have long warned about the need to incorporate probabilistic components into theories. One should never treat probability and statistics as a simple add-on to algebraic theory. Inadequate probabilistic specifications and inappropriate statistical tests, in turn, invite a host of artifacts. Very general mathematical and powerful statistical solutions for probabilistic specification and testing have recently started to emerge.

**Social Choice**

How is it possible to know what is best for a group of people when its members disagree with one another? In contemporary society people constantly search for a consensus that can satisfy everybody. A winner in a presidential election, a choice of the optimal policy in a large business organization, and a decision on the allocation of resources in a professional organization are just a few examples. Because of the nature of these high-stake decisions a variety of opinions are expressed in the group but only one can be chosen as a group decision.

The area of theoretical Social Choice provides us with bearish answers that a consensus may be unobtainable and that any group choice may be impugnable. Even worse, the choice of the best option may depend on the choice of the aggregation procedure. Nevertheless, the analysis of real-world data routinely argues against these theoretical predictions: the outcomes of voting procedures on real electorates agree remarkably well. This contradiction has puzzled researchers for decades. To solve this puzzle we propose novel models of electorates that explain the agreement among voting rules in real-world electorates, as well as the potential for mismatch among outcomes of various voting rules in popular articial domains.