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The 2N-ary Choice Tree Model for N-Alternative Preferential Choice.

Wollschläger LM, Diederich A - Front Psychol (2012)

Bottom Line: It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process.Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision.A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

View Article: PubMed Central - PubMed

Affiliation: School of Humanities and Social Sciences, Jacobs University Bremen Bremen, Germany.

ABSTRACT
The 2N-ary choice tree model accounts for response times and choice probabilities in multi-alternative preferential choice. It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process. The model provides expected choice probabilities and response time distributions in closed form for optional and fixed stopping times. The theoretical background of the 2N-ary choice tree model is explained in detail with focus on the transition probabilities that take into account constituents of human preferences such as expectations, emotions, or socially influenced attention. Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision. The model is extended to deal with more than three choice alternatives. A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

No MeSH data available.


6-Ary tree for choice between three alternatives A, B, and C with decision thresholds θ+ = 2 and θ− = 2 and three-different sample paths that lead to choice of alternative B.
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Figure 4: 6-Ary tree for choice between three alternatives A, B, and C with decision thresholds θ+ = 2 and θ− = 2 and three-different sample paths that lead to choice of alternative B.

Mentions: Withdrawal of alternatives from a choice set traces back to the model of elimination by aspects (EBA model, Tversky, 1972). But whereas elimination is the only means to come to a decision in the EBA model, the 2N-ary choice tree model like the multi-alternative DFT (Roe et al., 2001) provides several ways to reach a decision. An alternative i is chosen either if its preference state exceeds or if all other alternatives have been withdrawn from the choice set or a combination of these two. Figure 4 shows three examples of walks that lead to the choice of alternative B from a set of three alternatives A, B, and C with global thresholds θ+ = 2 and θ− = −2. The leftmost walk represents direct choice of alternative B, the rightmost withdrawal of alternative C and subsequent choice of option B and the middle walk illustrates withdrawal of alternative A first and then of option C. Note that after withdrawal of one alternative, there are two-outgoing edges less from the respective vertex downward. Transition probabilities change accordingly, i.e., the withdrawn alternative is removed from the comparison procedure and its counter states no longer contribute to the counter-dependent component (cf. next section). This corresponds to an anew started information sampling process between the remaining alternatives and their previous counter states as initial values.


The 2N-ary Choice Tree Model for N-Alternative Preferential Choice.

Wollschläger LM, Diederich A - Front Psychol (2012)

6-Ary tree for choice between three alternatives A, B, and C with decision thresholds θ+ = 2 and θ− = 2 and three-different sample paths that lead to choice of alternative B.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3378970&req=5

Figure 4: 6-Ary tree for choice between three alternatives A, B, and C with decision thresholds θ+ = 2 and θ− = 2 and three-different sample paths that lead to choice of alternative B.
Mentions: Withdrawal of alternatives from a choice set traces back to the model of elimination by aspects (EBA model, Tversky, 1972). But whereas elimination is the only means to come to a decision in the EBA model, the 2N-ary choice tree model like the multi-alternative DFT (Roe et al., 2001) provides several ways to reach a decision. An alternative i is chosen either if its preference state exceeds or if all other alternatives have been withdrawn from the choice set or a combination of these two. Figure 4 shows three examples of walks that lead to the choice of alternative B from a set of three alternatives A, B, and C with global thresholds θ+ = 2 and θ− = −2. The leftmost walk represents direct choice of alternative B, the rightmost withdrawal of alternative C and subsequent choice of option B and the middle walk illustrates withdrawal of alternative A first and then of option C. Note that after withdrawal of one alternative, there are two-outgoing edges less from the respective vertex downward. Transition probabilities change accordingly, i.e., the withdrawn alternative is removed from the comparison procedure and its counter states no longer contribute to the counter-dependent component (cf. next section). This corresponds to an anew started information sampling process between the remaining alternatives and their previous counter states as initial values.

Bottom Line: It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process.Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision.A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

View Article: PubMed Central - PubMed

Affiliation: School of Humanities and Social Sciences, Jacobs University Bremen Bremen, Germany.

ABSTRACT
The 2N-ary choice tree model accounts for response times and choice probabilities in multi-alternative preferential choice. It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process. The model provides expected choice probabilities and response time distributions in closed form for optional and fixed stopping times. The theoretical background of the 2N-ary choice tree model is explained in detail with focus on the transition probabilities that take into account constituents of human preferences such as expectations, emotions, or socially influenced attention. Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision. The model is extended to deal with more than three choice alternatives. A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided.

No MeSH data available.