EXAMPLE 4: Borda count

EXAMPLE 4: An embodiment in the context of deciding about investment on technologies

Let’s assume a number of technical advisors are sending their recommendations to the Chief Information Officer (CIO) of a company for a huge investment on computer technologies from 4 different vendors with different infrastructures. The advisors express their opinion the form of preference lists. Each technology has risks and advantages therefore there a no majority observed in preferences of technical advisors. The CIO must decide on which technology the investment must be done.

Let’s assume that the CIO likes the Borda Count method as the collective choice procedure. The preferences about Technologies A , B, C and D are collected and aggregated to a set of given Weighted Preference Lists as shown in WPL (Weighted Preference Lists)  below:

Given WPL1:

42 B>D>C>A

10 C>D>A>B

18 A>B>D>C

30 A>C>D>B

The number in front of each preference list is the weight of that preference list, which in this case is the presentation of a combination of the number of technical advisors with that preference, and the confidence of CIO on those advisors. Using the Borda Count method, “Technology  B” would be selected.

Points for A=42×0+10×1+18×2+30*3=154

Points for B=42×3+10×0+18×2+30*0=162

Points for C=42×1+10×3+18×0+30*2=132

Points for D=42×2+10×2+18×1+30*1=152

Borda Count Ranked list: (B>A>D>C)

Applying one of the embodiments of this invention based on process 100, step 200, will invoke process 200 in FIG. 2b.  Step 300, using a copy of Weighted Preference Lists applying Borda Count, finds a Strong Alternative. According to calculations above, is created as shown below:

Strong Alternative: (B)

In step 400, the Weighted Preference Lists are analyzed without “Technology C”:

WPL without C:

42 B>D>A

10 D>A>B

18 A>B>D

30 A>D>B

Points for A=42×0+10×1+18×2+30×2=106

Points for B=42×2+10×0+18×1+30×0=102

Points for D=42×1+10×2+18×0+30×1=92

Borda Count Highest Ranked Alternative: (A)

This has a different highest ranking alternative than the Strong Alternative and leads to considering “Technology C” a spoiler.

The same preference Lists without “Technology D” will result:

WPL without D:

42 B>C>A

10 C>A>B

18 A>B>C

30 A>C>B

Points for A=42×0+10×1+18×2+30×2=106

Points for B=42×2+10×0+18×1+30×0=102

Points for D=42×1+10×2+18×0+30×1=92

Borda Count highest ranked alternative: (A)

This has a different highest ranking alternative than the Strong Alternative (B) and leads to considering “Technology D” a spoiler. It is found that “Technology C” and “Technology D” are both spoilers because they are not selected technologies but their removal changes the selected choice using the same Borda Count method. Therefore, C and D are added to the List of Spoilers.

List of Spoilers: {C,D}

In step 216, to create a sorted list of spoilers, process 100 is recursively applied using a copy of Weighted Preference Lists including only the spoilers.

Copy of WPL including only the spoilers:

42 D>C

10 C>D

18 D>C

30 C>D

Process 100 using Borda count produces an Independent Collective Choice Ordered List as shown below:

Independent Collective Choice Ordered List of Spoilers= (D>C)

C is the lowest ranked alternative in Independent Collective Choice Ordered List of Spoilers, and is considered as the least favored spoiler and is signed out from Weighted Preference Lists which will result the Weighted Preference Lists to be as shown below wherein signed alternatives are in lowercase letters:

WPL spoilers signed:

42 B>D>c>A

10 c>D>A>B

18 A>B>D>c

30 A>c>D>B

Step 300, using a copy of Weighted Preference Lists without C, applying Borda Count finds a Strong Alternative as shown below:

Copy of WPL without C:

42 B>D>A

10 D>A>B

18 A>B>D

30 A>D>B

Strong Alternative: (A)

In step 400, the Weighted Preference Lists excluding signed spoilers are analyzed and no spoilers are found. Therefore in step 208, the List of Spoilers will be found empty and in step 206, all the signs in Weighted Preference Lists are cleared and the last Strong Alternative found is determined to be:

Highest ranked alternative: A

In step 110, in process 100, “Technology A” will be selected as the Independent Collective Choice.

FIG. 2c is a flowchart showing the steps used in process 200 in some embodiments of this invention to find a preferred collective choice using given Weighted Preference Lists while restricting the impact of spoilers by making a ranked list of spoilers when deciding which spoilers should be signed out. In step 300, it can use a collective choice procedure that creates a ranked list of spoilers like Borda Count.

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

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 and the Strong Alternative last selected is the desired preferred collective choice outcome. If any spoiler is detected and List of Spoilers is not empty, step 219 will follow.

In step 219, a sorted list of spoilers, a ranked list of alternatives is made. Some embodiments of the invention generate a sequence of alternatives using given Weighted Preference Lists including only alternatives in the list of spoilers by applying one or more preferential voting methods selected from the group consisting of but not limited to: a Nanson’s method, a Baldwin method, a Ranked Pairs method, a Coombs’ method, a Schulze method, a Kemeny-Young method, a Condorcet scoring method, a Borda Count method, a Copeland’s method, a rating summation method, and a plurality method. Other embodiments apply a collective choice procedure repeatedly to make a ranked list of alternatives by applying process 300 shown in FIG. 3a or FIG. 3b using given Weighted Preference Lists including only alternatives in the list of spoilers. The result of step 219 is a ranked List of Spoilers shown as list 218.

In step 220, 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 Lists.

Then steps 300 and other steps in process 200 are repeated until no spoilers are detected.

FIG. 2d is a flowchart showing the steps used in process 200 by some embodiments of this invention to find a preferred collective choice using given Weighted Preference Lists while restricting the impact of spoilers with early termination option. This way a decision can be made after some spoilers are signed and before all the spoilers are signed and excluded to make faster decisions.

In step 300, a Strong Alternative is found using said set of Weighted Preference Lists excluding signed spoilers similar to what was explained for FIG. 2a.

In step 203, if a predetermined number of spoilers have been removed, a dead line has passed or based on some other criteria, the search for more spoilers stops and in step 206, signs will be cleared; otherwise search for spoilers will continue in step 400.

Steps 400, 208, 300 and 206 are performed the same as process explained in FIG. 2a.

FIG. 3a is a flowchart showing the steps used in process 300 by some embodiments of this invention for finding the highest ranked alternative as well as making a ranked list of alternatives using provided copy of Weighted Preference Lists by applying a collective choice procedure repeatedly. One of the advantages of this method over prior art is that it can create a ranked list of alternatives. Another one of many advantages is that it doesn’t simply use a preferential voting system to select one or more weak alternatives to eliminate. It creates a ranked list by applying a collective choice procedure removing highest ranked alternatives repeatedly before deciding which alternative is the lowest ranked alternative, then records and erases the lowest ranked alternative found in this way from said lists and repeats this process until it finds the highest ranked at the end. This process can use “collective choice procedures that declare a single winner” repeatedly to create a ranked List of Spoilers.

In step 302, an operational copy of the provided copy Weighted Preference Lists is made which is shown as list 303.

In step 305, it is verified that there are more than one alternative in the operational copy of Weighted Preference Lists. If there is only one alternative remaining, that alternative will be considered the highest ranked alternative.

If in step 305 more than one alternative are found in the operational copy of Weighted Preference Lists, then in step 310, a collective choice procedure is applied to find the best choice in said operational copy of Weighted Preference Lists. The collective choice procedure can be selected from the group consisting of but not limited to: a Nanson’s method, a Baldwin method, a Ranked Pairs method, a Coombs’ method, a Schulze method, a Kemeny-Young method, a Condorcet scoring method, a Borda Count method, a Copeland’s method, a rating summation method, and a plurality method.

In step 318, the chosen alternative is removed from operational copy of Weighted Preference Lists and then steps 305, 310 and 318 are repeated until only one alternative remains in the operational copy of Weighted Preference Lists.

In step 305, if there is only one alternative remaining, step 320 will follow. In step 320, it is checked if a ranked list is required and step 321 will add the remaining alternative at the top of ranked list of alternatives which is shown as list 322 and in step 323, it is erased from the provided copy of Weighted Preference Lists.

In step 324, it is decided whether to continue with 302. If there is no more alternatives in provided copy of Weighted Preference Lists, step 326 will be performed. If there are more than one alternative in provided copy of Weighted Preference Lists then the steps 302 to 324 are repeated with fewer and fewer number of alternatives in provided copy of Weighted Preference List.

In each round another alternative is selected to be added to the top of ranked list of alternatives. Some embodiments of process 300 that are searching for a collective choice set, can consider all the remaining alternatives in provided copy of Weighted Preference Lists as collective choice set when there is a predetermined number of alternatives remaining.

In step 326, the last remaining alternative is considered as the highest ranked alternative and the process is concluded. At the end of process 300 the operational and provided copy of Weighted Preference List are not needed any more.

Some embodiments of process 300 can use temporarily excluding techniques instead removing and erasing using a copy of the Weighted Preference Lists.

FIG. 3b is a flowchart showing the steps used in process 300 by some embodiments of this invention to find the highest ranked alternative as well as to make a ranked list of alternatives from a provided copy of Weighted Preference Lists by applying plurality collective choice procedure repeatedly.

In step 302, an operational copy of the provided copy of Weighted Preference Lists is made which is shown as list 303.

In step 305, it is verified that there are more than one alternative in the operational copy of Weighted Preference Lists. If there is only one alternative remaining, that alternative will be considered the highest ranked alternative.

If in step 305 more than one alternative are found in the operational copy of Weighted Preference Lists, then in step 312, the first choice of each preference list in said operational copy of Weighted Preference Lists is selected. In step 314, for each first choice selected, sum of the weight of said Weighted Preference Lists that have said first choice is calculated. In step 316, the alternative with the highest aggregated weight among said first choices is selected as the highest ranked alternative.

In step 318, the chosen alternative is removed from operational copy of Weighted Preference Lists and then steps 305 to 318 are repeated until only one alternative remains in the operational copy of Weighted Preference Lists.

In step 305, if there is only one alternative remaining, step 320 will follow. In step 320, it is checked if a ranked list is required and step 321 will add the remaining alternative at the top of ranked list of alternatives which is shown as list 322 and in step 323, it is erased from the provided copy of Weighted Preference Lists.

Some embodiments of process 300 can use temporarily excluding techniques instead removing and erasing using a copy of the Weighted Preference Lists.

In step 324, it is decided whether to continue with 302. If there is no more alternatives in provided copy of Weighted Preference Lists, step 326 will be performed. If there are more than one alternative in provided copy of Weighted Preference Lists then the steps 302 to 324 are repeated with fewer and fewer number of alternatives in provided copy of Weighted Preference List.

In each round another alternative is selected to be added to the top of ranked list of alternatives. Some embodiments of process 300 that are searching for a collective choice set, consider all the remaining alternatives in provided copy of Weighted Preference Lists as collective choice set when there is a predetermined number of alternatives remaining.

In step 326, the last remaining alternative is considered as the highest ranked alternative and the process is concluded. At the end of process 300 the operational and provided copy of Weighted Preference List are not needed any more.

Some embodiments of process 300 can use temporarily excluding techniques instead removing and erasing using a copy of the Weighted Preference Lists.


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