File:Cyclic preferences after Schumm 1987.gif
Cyclic_preferences_after_Schumm_1987.gif (793 × 285 pixels, file size: 5 KB, MIME type: image/gif)
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Summary
editDescriptionCyclic preferences after Schumm 1987.gif |
English: Color illustration of Schumm's example[1] of cyclic preferences.
The example assumes that more red colors[note 1] are preferred[note 2] over more blue colors,[note 3] but 9 and 5 are indistiguishable for the human eye,[note 4][note 5] as are 5 and 1. Furthermore it assumes that a triple (a,b,c) is preferred[note 6] over a triple (p,q,r) e.g. if a>p and b~q and c~r.[note 7] But this implies the following paradoxical preference cycle: (9,5,1) > (1,9,5) > (5,1,9) > (9,5,1). This cycle is illustrated in the picture, with each triple depicted as a column.
However, the leftmost column is identical to rhe rightmost one, so the preferences form a cycle. Notes:
References:
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Date | |
Source | Own work |
Author | Jochen Burghardt |
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