Ranked Pairs


EXAMPLE 3: An embodiment the invention, implementing process 100 using

Ranked Pairs, in a computerized decision support system used for deciding about the



production of a drug 


[223] The preferences about production of Drugs A , B and C are collected and aggregated   

to a set of given Weighted Preference Lists as shown in WPL (Weighted   

Preference Lists) below, also let’s assume that environmental circumstances dictate

that only one of the drugs can be mass produced and Ranked Pairs is the collective

choice procedure used.

[224] Given WPL:

[225] 40 B>C>A

[226] 32 C>A>B

[227] 28 A>B>C

[228] Using Ranked Pairs and sorting the candidates the process will be:

[229] AB=60, BA=40 therefore AB vector=20

[230] BC=68, CB=32 therefore BC vector=32

[231] AC=28, CA=72 therefore CA vector=44

[232] Since A is preferred over B, and B over C, and C over A, there is a cycle and

Ranked Pairs will remove the weakest vector which is AB and the result is that the   

collective preference will be (B>C>A) and ‘Drug B’ will be the drug that will be   


[233] However, when applying process 100 and using one of the embodiments of this

invention described in FIG. 2a, in step 200, if Ranked Pairs is used, in step 300, a

ranked list of alternatives called Strong Alternative is found as shown below:

[234] Strong Alternative: (B)

[235] In step 400, the Weighted Preference Lists are analyzed and it is found that the

‘Drug C’ is the only spoiler, because its removal changes the highest ranked alternative

to (A) when using the same Ranked Pairs method. Therefore, C is added to the List of

Spoilers. Notice that removing (A) doesn’t change the highest ranked alternative.

Therefore, the list of spoilers will be:

[236] List of Spoilers: {C}

[237] In step 214, C is found to be the least favored spoiler and is signed out from

Weighted Preference Lists which will result the weighted reference lists to be as

shown in the following WPL wherein signed alternative is in lowercase letter:

[238] Given WPL, C signed:


[239] 40 B>c>A

[240] 32 c>A>B

[241] 28 A>B>c

[242] In step 300, a Strong Alternative based on WPL excluding signed alternative is

found as shown in the following lists.

[243] A copy of Given WPL, C excluded for process 300:

[244] 40 B>A

[245] 32 A>B

[246] 28 A>B

[247] Using Ranked Pairs and sorting the candidates with the most points, results:

[248] AB=60, BA=40 and therefore, AB vector=20

[249] This results in the following Strong Alternative:

[250] Strong Alternative: (A)

[251] In step 400, the Weighted Preference Lists excluding signed spoilers are analyzed

but there can not be any spoilers between two alternatives. Therefore in step 208, the

List of Spoilers will be found empty and all the signs in Weighted Preference Lists are

cleared and the last Strong Alternative found, is determined to be:

[252] Preferred collective choice: (A)

[253] In step 110, in process 100, therefore ‘Drug A’ will be selected as the Independent

Collective Choice.

[254] ‘Drug A’ is called an Independent Collective Choice because the embodiments of 

this invention using Ranked Pairs would choose ‘Drug A’, if choice ‘Drug C’ was not 

introduced as an alternative, and will choose ‘Drug A’, if choice ‘Drug C’ is introduced 

as an alternative. 

[255] FIG. 2b is a flowchart showing the steps used in process 200 in some embodiments

of this invention to find a preferred collective choice using said Weighted Preference

Lists while restricting the impact of spoilers. It recursively uses steps in process 100,

when deciding which spoilers should be signed out, and will ensure that the existence

of irrelevant alternatives among spoilers, when finding the least favored spoiler, will

not influence the outcomes.

[256] Steps 300, 400, 206 and 208 are identical to FIG. 2a described before.

[257] In Step 208, if no spoiler is detected, step 206 will follow and any signs added in

the current process to the Weighted Preference Lists are cleared and the process is

concluded with the last found Strong Alternative considered as the desired preferred

collective choice. If any spoiler is detected and List of Spoilers is not empty, step 216

will follow.

[258] In step 216, to create a sorted list of spoilers, process 100 is recursively employed

to produce an Independent Collective Choice Ordered List using a copy of said

Weighted Preference Lists including only the alternatives in said List of Spoilers. If the

number of spoilers detected in List of Spoilers is greater than two then some of them






may act as spoilers for others. The outcome of step 216 is an Independent Collective
Choice Ordered List of Spoilers and is shown as list 215.



[259] In step 217, at least one of the lowest ranked spoilers in Independent Collective 
Choice Ordered List of Spoilers is signed out of Weighted Preference Lists. In some   

embodiments, if alternatives in a compound spoiler are the least favored alternatives,   

all members of the compound are signed out. Some embodiments sign all the members

of the compound spoiler if one of the members of a compound spoiler is the lowest

ranked alternative. Some embodiments sign a plurality or all of spoilers in said Independent

Collective Choice Ordered List of Spoilers, out of said Weighted Preference


[260] Then steps 300 and other steps in process 200 are repeated until no spoilers are





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