Using of Rectangular Stochastic Matrices for the Problem of Evaluating and Ranking Alternatives

The paper investigates the issue related to a possible generalization of the “state-probability of choice” model so that the generalized model could be applied to the problem of ranking alternatives, either individual or by a group of agents. It is shown that the results obtained before for the problem of multi-agent choice and decision making by majority of votes can be easily transferred to the problem of multi-agent alternatives ranking. On the basis of distributions of importance values for the problem of ranking alternatives, we can move on to similar models for the choice and voting with the help of well-known exponential normalization of rows.So we regard two types of matrices, both of which belonging to the sort of matrices named balanced rectangular stochastic matrices. For such matrices, sums of elements in each row equal 1, and all columns have equal sums of elements. Both types are involved in a two-level procedure regarded in this paper. Firstly a matrix representing all possible distributions of importance among alternatives should be formed, and secondly a “state-probability of choice” matrix should be obtained on its base. For forming a matrix of states, which belongs and the rows of which correspond to possible distributions of importance, applying pairwise comparisons and the Analytic Hierarchy Method is suggested. Parameterized transitive scales with the parameter affecting the spread of importance between the best and the worst alternatives are regarded. For further getting the matrices of choice probabilities, another parameter which reflects the degree of the agent’s decisiveness is also introduced. The role of both parameters is discussed and illustrated with examples in the paper.The results are reported regarding some numerical experiments which illustrate getting distributions of importance on the basis of the Analytic Hierarchy Process and which are connected to gaining the situation of dynamic equilibrium of alternatives, i.e. the situation when alternatives are considered as those of equal value.

What matters in making demand-based decisions: Time alone or difficulty too?

Which task is easier, doing arithmetic problems of specified form for some specified duration, or carrying a bucket of specified weight over some specified distance? If it is possible to choose between the “more cognitive” task and the “more physical” task, how are the difficulty levels of the tasks compared? We conducted two experiments in which participants chose the easier of two tasks, one that involved solving addition or multiplication problems (Experiment 1) or addition problems with different numbers of addends (Experiment 2) for varying amounts of time (in both experiments), and one that involved carrying a bucket of different weights over a fixed distance (in both experiments). We found that the probability of choosing to do the bucket task was higher when the bucket was empty than when it was weighted, and increased when the cognitive task was harder and its duration grew. We could account for the choice probabilities by mapping the independent variables onto one abstract variable, Φ. The functional identity of Φ remains to be determined. It could be interpreted as an inferred effort variable, subjective duration, or an abstract, amodal common code for difficulty.

Verification and Optimization of Metro Fare Clearing Models Based on Travel Route Reconstruction

How to verify and optimize metro fare clearing models efficiently and accurately is a research focus in metro operations. Metro fare clearing models are mostly based on probability distributions. In such models, the normal distribution of travel time corresponding to the section probabilities is used to calculate the route choice probabilities of passengers on a multi-route metro network. By integrating the operating mileage proportions of each metro line operator and the corresponding route choice probabilities, the fare clearing proportions are calculated for all the operators of the metro network. To verify the accuracy of the fare clearing proportions, we propose a travel route reconstruction approach based on cell phone data acquisition technique. With wireless access point (AP) sensors installed at transfer stations, the unique medium access control (MAC) address of the smart phone with Wi-Fi function turned on is recorded and transmitted to a data analysis platform. After matching the MAC address information with time and location, the travel route of the smart phone user is reconstructed. Then, the parameters in the fare clearing model are verified and optimized according to the travel route choice probabilities. The proposed methodology is applied in Hangzhou metro network for experiment, and the metro fare clearing model is verified and modified by reconstructing the actual travel routs of the local passengers.

Bayesian Analysis of Processed Information in Decision Making Experiments

In research on decision making, experiments are often analyzed in terms of decision strategies. These decision strategies define both which information is used as well as how it is used. However, often it is desirable to identify the used information without any further assumptions about how it is used. We provide a mathematical framework that allows analyzing which information is used by identifying consistent patterns on the choice probabilities. This framework makes it possible to generate the most general model consistent with an information usage hypothesis and then to test this model against others. We test our approach in a recovery simulation to show thatthe used information may be reliably identified AUC>= .90. In addition, to further verify the correctness we compare our approach with other approaches based on strategy fitting to show that both produce similar results.

Estimation of Link Choice Probabilities Using Monte Carlo Simulation and Maximum Likelihood Estimation Method

Studying the uncertainty of traffic flow takes significant importance for the transport planners because of the variation and fluctuation of temporal traffic flow on all links of the transport network. Uncertainty analysis of traffic flow requires identifying and characterizing two sets of parameters. The first set is the link choice set, which involves the Origin-Destination pairs using this link. The second set is the link choice probabilities set, which includes proportions of the travel demand for the Origin-Destination pairs in the link choice set. For this study, we developed a new methodology based on Monte Carlo simulation for link choice set and link choice probabilities in the context of route choice modeling. This methodology consists of two algorithms: In the first algorithm, we used the sensitivity analysis technique the variance-based method to identify the set of Origin-Destination pairs in each link. In the second algorithm, we used a Gaussian process based on the Maximum Likelihood framework to estimate the link choice probabilities. Furthermore, we applied the proposed methodology in a case study over multiple scenarios representing different traffic flow conditions. The results of this case study show high precision results with low errors' variances.The key contributions of this paper: First, the link choice set can be detected by using sensitivity analysis. Second, the link choice probabilities can be determined by solving an optimization problem in the Maximum likelihood framework. Finally, the prediction errors' parameters of traffic assignment model can be modeled as a Gaussian process.