Welcome to an introduction to voting. In this lesson
we will define a preference ballot in a preference table
and also create a preference table, but before we do this
let's discuss some of the issues that can arise when selecting a winner of an
election sometimes voting is more involved than
just electing who gets the most votes there are several methods for
determining a winner of an election a certain method for selecting a winner
may be more appropriate based upon the type of election
for example the method of electing a president fairly
might be different than a group of friends fairly deciding what movie to
watch let's consider an example to see why
issues can arise when selecting winners of elections
let's begin by considering the following results from a student body presidential
election notice how the candidates are listed in
the first row from a through e and the second row tells us the number
of first place votes notice if we add the second row this
tells us there are a total of 450 votes and since
candidate e has the most votes at 102
e should win right well notice that in order to have a majority more than 50
percent somebody would have to have more than
225 votes and notice that no candidate here even
comes close to having a majority of the votes
now let's assume that the voters rank the candidates from their first choice
through their fifth choice and here are the results
and this is called a preference table which we'll define in just a moment
if we focus on candidate e for a moment notice how except for the 102
voted e as their first choice most voters really seem to dislike the
candidate because candidate e is ranked fifth for
everyone else
if we compare candidate e to candidate b notice how 98 people voted b
as their first choice only four less than e
but everyone else that didn't vote b first
ranked b second
so we could say that b is not disliked by anybody
so maybe that means that b should win it's situations like these
that lead to interesting discussions about voting theory and voting methods
and in this series of videos we'll be discussing various voting methods
but for this introductory video let's begin by defining
a preference ballot and a preference schedule or preference table
a preference ballot is a ballot in which the voters rank the choices
in order of preference and a preference schedule or table
is when these individual ballots are typically combined into one preference
scheduler table which shows the number of voters
in the top row that voted for each option
let's take a look at an example a college survey students about a possible
new design for their website the three sites are labeled a b and c
and the individual ballots are shown below
so these ballots here would be called the preference ballots
notice how the ballots rank the choices from first through third we're first
asked how many students voted well notice how we have three rows of
seven so we can say that 21 students voted
and then from these ballots we can create a preference table
where we'll list the choices from first through third then the number of voters
in the first row that voted for each order and since
there are three choices there are a total of three factorial
or six possible orders of preference we can also use the counting principle
and say there are three options for the first choice two options
for the second choice and one option for the third choice
giving us a total of six different orders
for the choices let's begin by listing the six possible orders
so if we start with a b c let's now list a c b
now let's start with b so we could have b a c
and then b c a and now we'll start with c
we could have c a b and then c b a
and now we'll count the number of votes for each particular order
let's begin by looking for the order of abc
there's 1 2 3 4 and five
now we'll look for acb here's one
two three so there's three voters for the order of
acb
now we'll look for bac there's one two
looks like there's only two and now we'll look for bca
there's one
two three
and four
now we'll look for c a b there is one two three and four
which leaves three 4c ba
now to make sure we didn't miss any let's go ahead and find this sum
to make sure the sum is 21. so we have plus three plus two that's ten plus four
plus three plus four which is 21. so again these are the preference
ballots and this is the preference table so based upon the voting method we would
normally use this preference table here to gather the information needed to
select the winner i hope you found this introduction
helpful