We introduce a distinction between two types of preference, time and temporal. We build a logic s... more We introduce a distinction between two types of preference, time and temporal. We build a logic similarly to Van Benthem[9] to capture the semantical differences. Instead of indexing agents like [9], we index temporally the worlds and preference relations. This allows us to express both statements of temporal preferences and time preferences. We show for a class of particular agents, it is possible to remove the index of temporal preferences while preserving all interpretations. We present two natural views on how temporal decision making should be made and show that given the most general characterization, the decision rules are identical.
The independence axiom (IA) takes two forms, in the context of WARP, and in the context of expect... more The independence axiom (IA) takes two forms, in the context of WARP, and in the context of expected utilities. In the first form, it states the the addition of an irrelevant alternative in a choice set does not change an agent's choice. This is subject to many counterexamples. The following paper argues IA is problematic due to current formalization of decisions being merely quantitative. We use a model of modal preference logic which accounts for qualitative elements and show that it solves the problematic scenarios. We then present some benefits of the model, in particular that it accounts for conditional preference in an explanatory manner.
We develop a formal system for the analysis of interpersonal preference comparison for pairs of a... more We develop a formal system for the analysis of interpersonal preference comparison for pairs of agents. This system is built on previously existing systems of preference logic which captures the semantics of single agent preference orders. The system expands on that and is able to produce a non-strict partial ordering which is complete and transitive given two restrictions. In other words, when given the preference orderings of two agents, our system allows us to form a binary relation such as “A’s preference for state x is stronger or equal to B’s preference for state y” where x and y are characterized as bundles of goods in Rn.
In this paper, we analyze possible ways for Bundle Theory (BT) to deal with the Problem of Indivi... more In this paper, we analyze possible ways for Bundle Theory (BT) to deal with the Problem of Individuality. Namely, what kind of restrictions should be placed on sets of qualities such that they result in bundles that are necessarily individuals. This paper introduces the problem and shows that the very consistency of BT depends on the possibility of a solution. It then analyzes traditional attempts such as the use of haecceity, compresence relations and tropes to conclude that they fail to offer a proper solution. Before proposing a solution, we analyze two successful but costly solutions by Van Cleve[5] and Losonsky[6] that most would be unwilling to accept. We conclude with our solution which employs “ownership”, a relation between the bundle and its parts, to define individuality.
In Jun Shao (1995), it is shown that a consistent bootstrap model selection (BMS) procedure can b... more In Jun Shao (1995), it is shown that a consistent bootstrap model selection (BMS) procedure can be obtained by minimizing the bootstrap estimates of the prediction error. However, for consistency, one must bootstrap a sample of size m which is less than the original sample size of N. The method is consistent when m → ∞ and m/N → 0. The optimal choice of m depends on the true parameters and can greatly impact the viability of the selection procedure. Here, we present a two-step bootstrap model selection (2SBMS) process which avoids the problem of having to select an optimal m.
We study player decision in the popular online video game League of Legends. In this game, player... more We study player decision in the popular online video game League of Legends. In this game, players make decision between 133 'champions' to play. Their decision is based observable variables such as pro-play and winrates but also unobserved variables such as attractiveness. Given their choices, the players may decide to purchase items for the champions they play. In this paper, we analyze the different factors impacting the 'pickrate' of the champions. In particular we use factor analysis to estimate the unobserved attractiveness of a champion.
We study the problem of matching student to courses. The main problem with current system is its ... more We study the problem of matching student to courses. The main problem with current system is its inability to account for student preferences. Furthermore, the system is logistically inefficient. We look specifically at cases of simultaneous enrollment. Namely, we provide an auction style mechanism for assignment of courses to students in the same enrollment time which does not suffer from the same flaws. We show that, with some natural assumptions, produces more expected utility per course. Lastly, we propose some additions to alleviate for unequal strategizing abilities among students .
Current epistemic logic models are mostly limited to either binary or prob-abilistic interpretati... more Current epistemic logic models are mostly limited to either binary or prob-abilistic interpretation of knowledge. We present a logic which allows for degrees/strength of knowledge/knowing independent of probabilities. Namely, we assign fuzzy values to both the atomic propositions and accessibility relationships. We first discuss why a fuzzy approach is necessary in some scenarios. Then we present the static and dynamic version of the logic. Lastly we use it to model a logically non-omniscient agent's knowledge over a decidable theory to illustrate the usefulness and some philosophical issue of the logic.
We introduce a distinction between two types of preference, time and temporal. We build a logic s... more We introduce a distinction between two types of preference, time and temporal. We build a logic similarly to Van Benthem[9] to capture the semantical differences. Instead of indexing agents like [9], we index temporally the worlds and preference relations. This allows us to express both statements of temporal preferences and time preferences. We show for a class of particular agents, it is possible to remove the index of temporal preferences while preserving all interpretations. We present two natural views on how temporal decision making should be made and show that given the most general characterization, the decision rules are identical.
The independence axiom (IA) takes two forms, in the context of WARP, and in the context of expect... more The independence axiom (IA) takes two forms, in the context of WARP, and in the context of expected utilities. In the first form, it states the the addition of an irrelevant alternative in a choice set does not change an agent's choice. This is subject to many counterexamples. The following paper argues IA is problematic due to current formalization of decisions being merely quantitative. We use a model of modal preference logic which accounts for qualitative elements and show that it solves the problematic scenarios. We then present some benefits of the model, in particular that it accounts for conditional preference in an explanatory manner.
We develop a formal system for the analysis of interpersonal preference comparison for pairs of a... more We develop a formal system for the analysis of interpersonal preference comparison for pairs of agents. This system is built on previously existing systems of preference logic which captures the semantics of single agent preference orders. The system expands on that and is able to produce a non-strict partial ordering which is complete and transitive given two restrictions. In other words, when given the preference orderings of two agents, our system allows us to form a binary relation such as “A’s preference for state x is stronger or equal to B’s preference for state y” where x and y are characterized as bundles of goods in Rn.
In this paper, we analyze possible ways for Bundle Theory (BT) to deal with the Problem of Indivi... more In this paper, we analyze possible ways for Bundle Theory (BT) to deal with the Problem of Individuality. Namely, what kind of restrictions should be placed on sets of qualities such that they result in bundles that are necessarily individuals. This paper introduces the problem and shows that the very consistency of BT depends on the possibility of a solution. It then analyzes traditional attempts such as the use of haecceity, compresence relations and tropes to conclude that they fail to offer a proper solution. Before proposing a solution, we analyze two successful but costly solutions by Van Cleve[5] and Losonsky[6] that most would be unwilling to accept. We conclude with our solution which employs “ownership”, a relation between the bundle and its parts, to define individuality.
In Jun Shao (1995), it is shown that a consistent bootstrap model selection (BMS) procedure can b... more In Jun Shao (1995), it is shown that a consistent bootstrap model selection (BMS) procedure can be obtained by minimizing the bootstrap estimates of the prediction error. However, for consistency, one must bootstrap a sample of size m which is less than the original sample size of N. The method is consistent when m → ∞ and m/N → 0. The optimal choice of m depends on the true parameters and can greatly impact the viability of the selection procedure. Here, we present a two-step bootstrap model selection (2SBMS) process which avoids the problem of having to select an optimal m.
We study player decision in the popular online video game League of Legends. In this game, player... more We study player decision in the popular online video game League of Legends. In this game, players make decision between 133 'champions' to play. Their decision is based observable variables such as pro-play and winrates but also unobserved variables such as attractiveness. Given their choices, the players may decide to purchase items for the champions they play. In this paper, we analyze the different factors impacting the 'pickrate' of the champions. In particular we use factor analysis to estimate the unobserved attractiveness of a champion.
We study the problem of matching student to courses. The main problem with current system is its ... more We study the problem of matching student to courses. The main problem with current system is its inability to account for student preferences. Furthermore, the system is logistically inefficient. We look specifically at cases of simultaneous enrollment. Namely, we provide an auction style mechanism for assignment of courses to students in the same enrollment time which does not suffer from the same flaws. We show that, with some natural assumptions, produces more expected utility per course. Lastly, we propose some additions to alleviate for unequal strategizing abilities among students .
Current epistemic logic models are mostly limited to either binary or prob-abilistic interpretati... more Current epistemic logic models are mostly limited to either binary or prob-abilistic interpretation of knowledge. We present a logic which allows for degrees/strength of knowledge/knowing independent of probabilities. Namely, we assign fuzzy values to both the atomic propositions and accessibility relationships. We first discuss why a fuzzy approach is necessary in some scenarios. Then we present the static and dynamic version of the logic. Lastly we use it to model a logically non-omniscient agent's knowledge over a decidable theory to illustrate the usefulness and some philosophical issue of the logic.
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