Machine decisions based on preferential voting techniques
First Claim
1. A method of computing an aggregate decision about an object, the method comprising:
- obtaining at least two intermediate rankings, each of which ranks at least three alternatives with respect to the object;
initializing at least two series of preferences, wherein each series corresponds to one of the intermediate rankings, each series is ordered from a first preference to a last preference, each series initially groups each alternative into one of the preferences selected based on the corresponding intermediate ranking, and each preference includes at least one of the alternatives;
selecting, based on the preferences, at least one of the alternatives as a weak alternative;
removing at least one weak alternative from each series;
then re-grouping each series into preferences based on the intermediate ranking corresponding to the series;
deciding, when each series contains less than a first threshold number of the alternatives, that the aggregate decision includes the alternatives remaining in the series; and
repeating selecting, removing, re-grouping, and deciding until an aggregate decision is made.
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Abstract
A method and apparatus for computing an overall or aggregate decision based on intermediate decisions as to which of a set of alternatives best characterize an object. The alternatives are partitioned into at least two series of preferences corresponding to at least two intermediate rankings. Various embodiments may base the intermediate rankings on: a machine learning technique; a decision tree; a belief network; a neural network; a static model; a program; or an evolutionary training method. Based on the preferences, a weak alternative is selected and removed from the series. The selection of the weak alternative may include identifying which alternatives lose pairwise to the other alternatives, are excluded from the first preferences, are included in the last preferences, or have a lowest average preference ranking. The selecting and removing continue until the remaining alternatives are the aggregate decision. Various embodiments may be applied to classification problems, prediction problems or selection problems.
24 Citations
30 Claims
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1. A method of computing an aggregate decision about an object, the method comprising:
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obtaining at least two intermediate rankings, each of which ranks at least three alternatives with respect to the object;
initializing at least two series of preferences, wherein each series corresponds to one of the intermediate rankings, each series is ordered from a first preference to a last preference, each series initially groups each alternative into one of the preferences selected based on the corresponding intermediate ranking, and each preference includes at least one of the alternatives;
selecting, based on the preferences, at least one of the alternatives as a weak alternative;
removing at least one weak alternative from each series;
thenre-grouping each series into preferences based on the intermediate ranking corresponding to the series;
deciding, when each series contains less than a first threshold number of the alternatives, that the aggregate decision includes the alternatives remaining in the series; and
repeating selecting, removing, re-grouping, and deciding until an aggregate decision is made. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
one of the alternatives that is in the first preference of at least a second threshold number of the series;
one of the alternatives that is preferred over every other alternative in every series; and
one of the alternatives that is preferred over at least a first percentage of the alternatives in at least a second percentage of the series.
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20. The method of claim 1, wherein the first threshold number is selected from a predetermined number, a predetermined percentage of the alternatives, and a number that is adjusted during the operation of the method.
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21. A computer readable media containing instructions that, when the instructions are read and executed by a system, control a process comprising:
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obtaining at least two intermediate rankings, each of which ranks at least three alternatives with respect to the object;
initializing least two series of preferences, wherein each series corresponds to one of the intermediate rankings, each series is ordered from a first preference to a last preference, each series initially groups each alternative into one of the preferences selected based on the corresponding intermediate ranking, and each preference includes at least one of the alternatives;
selecting, based on the preferences, at least one of the alternatives as a weak alternative;
removing at least one weak alternative from each series;
thenre-grouping each series into preferences based on the intermediate ranking corresponding to the series;
deciding, when each series contains less than a first threshold number of the alternatives, that the aggregate decision includes the alternatives remaining in the series; and
repeating selecting, removing, re-grouping, and deciding until an aggregate decision is made. - View Dependent Claims (22, 23, 24, 25, 26, 27, 28)
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29. An apparatus configured to compute an aggregate decision about an object, the apparatus comprising:
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an interface configured to obtain at least two intermediate rankings, each of which ranks at least three alternatives with respect to the object;
a processor configured to initialize at least two series of preferences, each series corresponding to one of the intermediate rankings, each series being ordered from a first preference to a last preference, each series initially grouping each alternative into one of the preferences selected based on the corresponding intermediate ranking, and each preference including at least one of the alternatives;
wherein the processor is further configured to select, based on the preferences, at least one of the alternatives as a weak alternative, to remove the weak alternative from each series, to accordingly re-group each series into preferences based on the intermediate ranking corresponding to the series, to decide, when each series contains less than a threshold number of the alternatives, that the aggregate decision includes the alternatives remaining in the series, and to repeat the selecting, the removing, the re-grouping, and the deciding until an aggregate decision is made.
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30. A means for computing an aggregate decision about an object, the means comprising:
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a means for obtaining at least two intermediate rankings, each of which ranks at least three alternatives with respect to the object;
a means for initializing at least two series of preferences, each series corresponding to one of the intermediate rankings, each series being ordered from a first preference to a last preference, each series initially grouping each alternative into one of the preferences selected based on the corresponding intermediate ranking, and each preference including at least one of the alternatives;
a means for selecting, based on the preferences, an alternative as a weak alternative;
a means for removing the weak alternative from each of the series, and accordingly re-grouping each series into preferences based on the intermediate ranking corresponding to the series;
a means for deciding, when each series contains less than a threshold number of the alternatives, that the aggregate decision includes the alternatives remaining in the series; and
a means for repeating the selecting, the removing, the re-grouping, and the deciding until an aggregate decision is made.
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Specification