MATH 10 VOTING SYSTEM AND APPORTIONMENT

AMS Meeting

NOOO! I don’t want to That’s corny, I want something
watch a horror movie, how more thrilling like F9.
about the sequel to Avatar?

Good day! I’m sure you’ve all
heard about the block-

screening that will be held
next month. We’ve decided to

watch The Conjuring.

Why not a Marvel movie No! The Conjuring is the
like The Eternals or best movie for
Shang-chi? screening!

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Enough!! Let’s just vote among those five Movies:
movies. The options for the five movies The Eternal
will be all of the movies that you have
said. You will rank the movies listed from F9
1 to 5, 1 being your first choice while 5 Avatar 2
Shang-chi
being your last choice. The Conjuring

How will we know what I’ll tell you after compiling
movie will be screened? the votes.

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We’ve gathered 450 votes Let’s use what we’ve learned from
from all of the members that
Voting Systems our MATH 10 classes, the different
are present today. voting systems. The movie with the
most number of wins from the

different voting systems will be the

movie to be shown next month.

Based on the plurality method, Yay! My movie won!! We’re not yet done. There
the movie with the highest are other voting systems to

number of votes will win. Thus, be considered.
F9 wins with 139 votes.
Voting S

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What are the other voting There are still Sequential
systems that need to be Voting, Borda Count Method,

considered? Condorcet Method, and
Approval Voting.

Moving on to the next voting system Winner’s Run-off is done by pitting the two movies
which is sequential voting. We have with the highest number of first place votes. In this
conducted two ways to know the winner case, the two movies with the highest number of
for this voting system, one is Winners votes are F9 and Shang-Chi. We tested the number of
Run-Off and the other is Loser-Eliminated. votes of F9 over Shang-Chi and the number of votes
of Shang-Chi over F9. After careful deliberation, F9

wins with 239 votes.

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Losers-eli For loser-eliminated, we determined the F9 Yes!! That’s 2 overall
number of first place votes of each option, wins wooh!!
and then we eliminated the one with the least
number of first place votes. This went on until
there was only one movie left. The last movie

standing is: the F9.

Okay, the next thing that we did The pointing system that we Borda Count Winner:
is the Borda Count system. In implemented for the 1st, 2nd, 3rd, Avatar 2
the Borda Count system, we
4th, and 5th votes are 5 points
assigned points to each each, 4 points each, 3 points each,
position in the ranking.
2 points each, and 1 point each
respectively.

The winner that we got from
implementing the Borda
Count method is Avatar 2
with a total of 1577 votes.

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Well, here we go!! Borda Count Awww, it’s fine. F9 has
Avatar 2 for the win!! Avatar 2 2 overall wins so I
won’t be bothered.

F9 Hmmm.. let’s see. The next voting There are 10 possible pairs from the
system that we did is the Condorcet movies above after using the
Method. In this method, it is required
to pair each movie as it is a pairwise combination method. So, after pairing
them, we tested the number of votes of
voting.
each candidate over the other
Then, the candidate with the most candidate in the pair.
number of wins out of all the pairs
will be the winner. So, the result is
F9 wins with 4 wins out of the 10

pairs!

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F9 3 overall wins!! Just Next method that we implemented is
one more! the approval voting. In this case, the
3 wins candidates are ranked according to the
number of approval votes that they’ve
gotten. The candidate with the most

approval vote wins.

We chose the top 2 movies So, after carrying out the
with the approval votes, and approval process, F9 still wins
then find out which of these
two have the highest number of with a total of 250 votes.

F9approval votes.
250 votes

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F9 4 overall wins!! That Yes, after doing all of
settled it right? the voting systems, the
4 wins F9 won in most of the

voting system.

So, for the movie Aww, it’s fine, maybe I can Yes!! I am so excited.
screening, we will watch convince others to watch
the Fast and Furious 9. F9 Marvel movies at the next

4 wins movie screening.

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Wait, it’s good that the movie What is it? Is the movie
for the movie screening is unavailable?

already settled. However, there F9
is actually one problem. 4 wins

No, the venue for the movie
screening has only 200 seats,
we have 450 members here so
we can’t accommodate all of

them.

Oh no!! I’m the one who What shall we do? I also want
suggested that so I must be to watch it.

included!!

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Meh, I don’t care about it. Ha, I thought that the problem ends
there. Wait, I remembered that we
can also apply one of the lessons
that we have in our Math 10 class?

Apportionment, right?

Oh, yes! We can use Okay, should we use all of the Apportionment
apportionment to know the apportionment method or should
allocation of seats to the we just select one apportionment

members of our org! method?

Hmm,, I think that we
should use all of them.

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Okay. So, the first apportionment Oh, I remember what to do in this method!
method that I can remember is the In Hamilton method, each group is given an
Hamilton Method. Wait, what should initial allotment equal to the lagest integer
not exceeding its quota. If there are extra
we do in the Hamilton method seats, these are distributed one at a time to
again?
the groups ordered by the size of the
fractional part of the quotas.

Hmm,, okay. So, what will Let’s just choose the year level
be the groups for this? of our members. Freshmen,
Sophomores, Juniors, and
Seniors for this. Apportionment

Okay, noted. How will we do
the Hamilton method again? I

don’t understand what he
said earlier.

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First thing to do in the Hamilton's How will you compute Octob
the quota for each
Method is to first compute the total group? 2

population. In this case, we have 450
members so that will serve as the total

Hamilton'spopulation. According to LH, the
available seats are 200. After that, we method
will compute the quota group.

Well--

I know, I know!! To compute the quota of each

group, we multiply the available seats by the ratio

of the group’s population to the total population. Oh, I see. ThOen,ctober

So, for example in the freshmen, we multiply the 29what will we do
available seats which is 200 to the ratio of the next?

Hamilton'sfreshmen population to the entire population.
That will be equal to 69.33. This will also be method
applied to other year levels as well!

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After that, we get the largest integer not Hamilton'sHmmm,, I already forgot
exceeding the quota. This integer will be the method what to do.

initial allotment. We will do this on the
succeeding year level. After knowing the initial
allotment of each year level, we will now get the
sum of the initial allotment. If the sum is equal to

the available seats, then our job is done.

What if it isn’t?

If the sum of the initial allotment is not equal Wait, based on the table, the one

to the available seats, then we will compute with the highest fractional part in Octob

how many seats more or less to reach the their quota is the sophomore! So, 2
we will add 1 on their initial
Hamilton'snumber of seats available. On our data, we allotment right?
still need 1 more. So, we will order the
fractional parts of the quota. The one with the
methodhighest fractional part will have additional
allotment.

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Yes! So that will bring us Freshmen Octob

who can have 69 seats, Sophomore Ohh, I get it. 2

who can have 65 seats, Junior who

Seatscan have 32 seats, and Seniors who
can have 34 seats.
Freshmen - 69

Sophomore - 65

Junior - 32

Seniors - 34

Wow, that’s good Freshmen Oh yes, we can have
considering I’m a Sophom 65 seats.
Junior
freshman. Seniors

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Aw, only 32 seats? men - 69 Wait, don’t be too hasty. October
That’s not enough. omore - 6a5pTphoertrieonamreesnttilml oetthheords
or - 32 that need to be done. 29

iors - 34

What are they? The next method that we will be Jefferson's
doing is the Jefferson’s Method. Method
The Jefferson’s method is quite

different from Hamilton’s
method.

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How is it different? Jefferson’s method chooses a divisor (d) October
for the population so that rounding down
29
the modified quotas will yield to
apportionment. This will help us to find
the allocated seats that will be available

for each year level.

So, Jefferson's method will Wait, I remember this just d = 450/200
use a divisor . How will we now. To get the divisor, we
compute for the divisor? will divide the total population

to the number of seats
available. Is that right, Pres?

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Yes, it is! Then, what will we do Ateneo
next? Memer
Society

We will divide the population of Okay, so we can get the quota for Ateneo
each group, in our case the year the freshmen year level by Memer
dividing the population of Society
level, to the divisor which will
yield the quota. The divisor for freshmen to the divisor, right?

our data is 2.25.

d = 2.25

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Yes, that’s right. Remember to So, the freshmen should
apply the same principle to have a 69.33 in their
other year levels as well. quota.

While sophomores should Wait, how will we do the Ateneo
have 64.44 in their quota. initial allotment for each Memer
Society
group?

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To know the initial allotment for Oh, I see. So this will
each group, we will round down use the rounding down

the quota of each group. For method.
example, freshmen who have
69.33 in their quota will now have

69 initial allotment.

69. 33 -> 69

Yes! After that we will also take In our case, the divisor will be Ateneo
the sum of the initial allotment. If adjusted until it reaches the Memer
it’s not the same as the number of number of seats available right? Society
seats available, we will adjust the
divisor so that modified quotas
will produce an apportionment.

h = 200

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Yes! Jefferson'sSo, what will be the allocation Ateneo
of seats to each level after Memer
Methodapplying Jefferson’s method? Society

I’ve computed this and I got 69 What? That’s the same 69 seats- Freshmen
seats for Freshmen, 65 seats for apportionment that we got from 65 seats- Sophomores
Sophomore, 32 seats for Junior
Hamilton’s method, right? 32 seats- Junior
and 34 seats for Seniors. 34 seats- Senior

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AMS 69 seats- Freshmen Let’s see if it’s the same
BEST 65 seats- Sophomores for other
ORG! Yes, it is!
32 seats- Junior apportionment methods.
34 seats- Senior What are other apportionment

methods, Pres?

The next apportionment method that we Webster's AMS
will use is the Webster’s method. Method
So, in the case of BEST
It is fairly similar to Jefferson’s method since sophomores
it also uses the divisor but the only difference is ORG!
that Webster's method rounded off the quota
with 65.44 votes, it will be 65
of each group to get its initial allotment.

right?

AMS Meeting

Okay, I solved it! There will be a

total of 69 seats

Yes! And if the sum of the initial Webster's 69 seats- Freshmen for Freshmen, 65 seats for
allotment is not the same as the Method
available seats, we will adjust the 65 seats- Sophomores Sophomore, 32 seats for Junior
divisor until we get the exact answer and 34 seats for Seniors.
that we want which is 200 seats. 32 seats- Junior

34 seats- Senior

Still the same apportionment Adam's There’s still one more method which is
that we got by using Method
Jefferson’s method. AMSAdam's method. It is fairly similar to Jefferson’s
method and Webster’s method since it also

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Adam's Adam's Yes, you’re right!
Method Method
So, instead of rounding off or rounding
down, this method will round up the
quota.

So, in the freshmen case Yes! AMS
with a quota of 69.33, the BEST
initial allotment will be 70? 69. 33 -> 70 ORG!

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AMS 69 seats- Freshmen That’s right. Adjust
BEST Then if the sum of the ini6ti5al seats- Sophomores and adjust until you
ORG! allotment is not equal to the num3be2r seats- Junior
of seats athveaildaibvilseo, rwuentwililwl ceognetitn3tuh4ee get it!
to adjust seats- Senior

available seats, right?

That’s the same as Oh, I get it. I got 69 seats for 69 seats- Freshmen
the other method that Freshmen, 65 seats for 65 seats- Sophomores

we used. Sophomore, 32 seats for Junior 32 seats- Junior
and 34 seats for Seniors. 34 seats- Senior

AMS Meeting

Phew, now we solved our Movie I look forward to the Ateneo
problems. Screening movie screening! Memer
Society

Movie Ateneo Movie Ateneo
ScMreetoeon. ing Memer Memer
Me too. Society ScreenTthoiadntaeygn! dBse the meeting for Society
sure to attend
Me too.
the movie screening!

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PRESIDENT STUDENT 2

SECRETARY STUDENT 5

LOGISTICS HEAD

STUDENT 4

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