method, in a computerized decision support system used for deciding about the production of a
Let’s assume 100 researchers have expressed their preferences about production of three drugs for
a disease. Each drug has benefits and side effects and different researchers have different
preferences. Also let’s assume that environmental circumstances dictate that only one of the drugs
can be mass produced and we want to use the plurality method for choosing the collective choice.
However, we also want to know in case that the production of the most preferred collective
choice became impossible what are the second and third preferred alternatives.
The preferences about Drugs A, B and C are collected and aggregated to a set given WPL
(Weighted Preference Lists) shown below:
The number in front of each preference list is the weight of that preference list which in this case
is the count of the researchers having that preference.
Although 60 researchers prefer Drug A over B, but the introduction of Drug C does change the
outcome. Many voting systems are prone to this flaw and say B is the collective choice. Plurality,
IRV, Ranked pairs, and Borda Count all select (B).
Applying process 100, using the plurality method which looks only at the first choice in
preference lists, Step 200 analyzes that ‘Drug if would be selected, but if ‘Drug C’ is removed
from Weighted Preference Lists then ‘Drug A’ will be the collective choice. Sixty people prefer
‘Drug A’ to ‘Drug B’ but the introduction ‘Drug C’ splits their vote and ‘Drug B’ is chosen as a
result. Here ‘Drug C’ is considered to be the spoiler. Drugs A and B don’t have this property. If
‘Drug A’ is removed ‘Drug B’ will be selected with even more preferences (no change in the
outcome) and ‘Drug B’ itself is not considered a spoiler based on the definition above. Step 200
will process the given lists without ‘Drug C’ to restrict the impact of the spoiler:
Given WPL, without C:
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And the highest ranked alternative will be determined to be:
Highest ranked alternative: A
In step 110, Drug N will be selected as the Independent Collective Choice.
In step 130, If only one Independent Collective Choice should be selected, ‘Drug A’ will be the
desired answer but in this example an ordered list of collective choices is desired; therefore, step
150 will be the next step.
In step 150, ‘Drug A’ will be added to the Independent Collective Choice Ordered List shown as
In step160, ‘Drug A’ will be deleted from Weighted Preference Lists resulting WPL shown below:
Given WPL, A deleted:
In step 170, it is decided that more alternatives must be selected and in step 200, Weighted
Preference Lists shown in WPL will be used but there can not be any spoilers between two
alternatives B and C, which will result in a highest ranked alternative as:
Highest ranked alternative: B
In step 110, B is selected as an Independent Collective Choice and in step 150, B will be add as
the next choice to Independent Collective Choice Ordered List 140, which results:
Independent Collective Choice Ordered List: (A>B)
In step 160, B is deleted from given Weighted Preference Lists resulting WPL shown below:
Given WPL, B deleted:
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will be selected as Independent Collective Choice and will be added as the next choice to
Independent Collective Choice Ordered List.
Independent Collective Choice Ordered List: (A>B>C)
This means that the best collective choice is the production of Drug N and the next choice is
‘Drug B’. ‘Drug A’ is called the Independent Collective Choice because the embodiments of this
invention using plurality method would choose ‘Drug A’ if choice ‘Drug C’ was not introduced as
an alternative and will choose ‘Drug A’ if ‘Drug C’ is introduced as an alternative.
The embodiments of this invention make the same decision before and after introduction of an
alternative except in situations like when the introduced alternative is so preferred that it becomes
the collective choice itself
Step 200 can be done differently in different embodiments of this invention. Different embodiment
of this invention can use different collective choice procedures while finding the highest ranked
alternative. For the example above, embodiments of this invention using any of plurality, Ranked
pairs, or Borda count all will choose (A>B>C) as Independent Collective Choice Ordered List
after they restrict the impact of the spoilers.
FIG. lb is a flow chart showing the basic steps used in process 100, according to some
embodiments of the invention. It finds an Independent Collective Choice or produces an
Independent Collective Choice Ordered List using a given set of Weighted Preference Lists.
In step 101, if the weight of one of the lists in given Weighted Preference Lists, is greater than
half of the total sum of weights of said given Weighted Preference Lists, in step 105, the
alternative at the top of that list is considered the Independent Collective Choice and that list is
considered the Independent Collective Choice Ordered List and is copied to list 140 and the
process 100 is concluded. If the weight of none of the lists is greater than half of the total sum of
weights, step 200 is performed. The rest of FIG. lb is exactly as FIG. la described above.
FIG. 2a 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.
In step 300, a highest ranked alternative called Strong Alternative is found using said set of
Weighted Preference Lists excluding signed spoilers. The Strong Alternative can be found by a
variety of methods or collective choice procedures and will be used as a reference point in next
steps. Signed spoilers are those alternatives that are detected in this process as spoilers in step 400
and are signed in step 214. At the first iteration of step 300, there is no signed spoiler.
To find the highest ranked alternative, some embodiments of the invention generate a sequence of
alternatives using given Weighted Preference Lists excluding signed spoilers by applying one or
more preferential voting procedures selected from the group consisting of but not limited to: a
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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 as shown in FIG. 3a or FIG. 3b using given
Weighted Preference Lists excluding signed spoilers. In many examples described hereafter,
where the repeated application of plurality in process 300 is used, collective choice procedures
could be used as well.
In step 400, the Weighted Preference Lists excluding signed spoilers are analyzed and a List of
Spoilers (list 204) is created. Some embodiments of this invention create an ordered List of
Spoilers as part of process 400 and some just create a set of spoilers. Each spoiler can be simple
(made of one alternative) or compound (made of a plurality of alternatives).
In Step 208, if no spoiler is detected, any signs added in the current process to the said Weighted
Preference Lists are cleared in step 206, and this process is concluded while the last Strong
Alternative found is considered as the desired preferred collective choice. If any spoiler has been
detected and List of Spoilers is not empty, step 214 will follow.
In step 214, the spoilers in the List of Spoilers are analyzed, and the least favored among them is
found and 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 least preferred alternative. Some embodiments sign a plurality or all of
spoilers in said List of Spoilers, out of said Weighted Preference Lists. Then steps 300, 400, 208
and the rest of steps are applied until no spoilers detected.