Even machine decisions based on preferential voting techniques like the method and apparatus proposed in patent 6,763,338 to Kirshenbaum, July 13, 2004 are susceptible to the problems mentioned above. For example, the content of table 420 of FIG. 4 (b) of above mentioned patent it is shown as the following Weighted Preference Lists (WPL):
And in the description of above mentioned patent, it is discussed that the method proposed has different results depending to the type of preferential voting technique used. Moreover, it can be shown that even using one preferential voting technique in Kirshenbaum’s invention will result in different decisions by introduction of irrelevant alternatives. The description explains that when alternatives with “Most Last Place Preferences” are removed repeatedly, “Burger” is selected as the aggregate decision.
But if another type of restaurant, for example “Sub”, is introduced and most of people don’t prefer it as shown below:
Sushi will be removed first; Then Pizza and then Sub will be removed. This will lead to
And “Salad” will be selected as the aggregate decision while introduction of Sub should not switch the choice between Burger and Salad.