Which voting system is the best? - Alex Gendler
-
0:07 - 0:10Imagine we want to build a new space port
-
0:10 - 0:13at one of four recently settled
Martian bases, -
0:13 - 0:17and are holding a vote
to determine its location. -
0:17 - 0:23Of the hundred colonists on Mars,
42 live on West Base, 26 on North Base, -
0:23 - 0:2815 on South Base, and 17 on East Base.
-
0:28 - 0:32For our purposes, let’s assume
that everyone prefers the space port -
0:32 - 0:37to be as close to their base as possible,
and will vote accordingly. -
0:37 - 0:40What is the fairest way
to conduct that vote? -
0:40 - 0:44The most straightforward solution
would be to just let each individual -
0:44 - 0:49cast a single ballot, and choose
the location with the most votes. -
0:49 - 0:54This is known as plurality voting,
or "first past the post." -
0:54 - 0:57In this case, West Base wins easily,
-
0:57 - 1:00since it has more residents
than any other. -
1:00 - 1:04And yet, most colonists would consider
this the worst result, -
1:04 - 1:07given how far it is from everyone else.
-
1:07 - 1:12So is plurality vote
really the fairest method? -
1:12 - 1:16What if we tried a system
like instant runoff voting, -
1:16 - 1:19which accounts for the full range
of people’s preferences -
1:19 - 1:22rather than just their top choices?
-
1:22 - 1:23Here’s how it would work.
-
1:23 - 1:27First, voters rank
each of the options from 1 to 4, -
1:27 - 1:30and we compare their top picks.
-
1:30 - 1:34South receives the fewest votes
for first place, so it’s eliminated. -
1:34 - 1:40Its 15 votes get allocated
to those voters’ second choice— -
1:40 - 1:44East Base— giving it a total of 32.
-
1:44 - 1:49We then compare top preferences
and cut the last place option again. -
1:49 - 1:51This time North Base is eliminated.
-
1:51 - 1:55Its residents’ second choice
would’ve been South Base, -
1:55 - 1:59but since that’s already gone,
the votes go to their third choice. -
1:59 - 2:05That gives East 58 votes over West’s 42,
making it the winner. -
2:05 - 2:08But this doesn’t seem fair either.
-
2:08 - 2:12Not only did East start out
in second-to-last place, -
2:12 - 2:16but a majority ranked it among
their two least preferred options. -
2:16 - 2:21Instead of using rankings, we could try
voting in multiple rounds, -
2:21 - 2:25with the top two winners
proceeding to a separate runoff. -
2:25 - 2:29Normally, this would mean West and North
winning the first round, -
2:29 - 2:31and North winning the second.
-
2:31 - 2:34But the residents of East Base realize
-
2:34 - 2:36that while they don’t have
the votes to win, -
2:36 - 2:39they can still skew the results
in their favor. -
2:39 - 2:43In the first round, they vote
for South Base instead of their own, -
2:43 - 2:46successfully keeping North
from advancing. -
2:46 - 2:50Thanks to this "tactical voting"
by East Base residents, -
2:50 - 2:55South wins the second round easily,
despite being the least populated. -
2:55 - 3:00Can a system be called fair and good
if it incentivizes lying -
3:00 - 3:02about your preferences?
-
3:02 - 3:06Maybe what we need to do
is let voters express a preference -
3:06 - 3:09in every possible head-to-head matchup.
-
3:09 - 3:12This is known as the Condorcet method.
-
3:12 - 3:15Consider one matchup:
West versus North. -
3:15 - 3:19All 100 colonists vote on their preference
between the two. -
3:19 - 3:24So that's West's 42 versus
the 58 from North, South, and East, -
3:24 - 3:26who would all prefer North.
-
3:26 - 3:29Now do the same
for the other five matchups. -
3:29 - 3:33The victor will be whichever base
wins the most times. -
3:33 - 3:37Here, North wins three
and South wins two. -
3:37 - 3:40These are indeed the two
most central locations, -
3:40 - 3:46and North has the advantage of not being
anyone’s least preferred choice. -
3:46 - 3:51So does that make the Condorcet method
an ideal voting system in general? -
3:51 - 3:53Not necessarily.
-
3:53 - 3:56Consider an election
with three candidates. -
3:56 - 4:02If voters prefer A over B, and B over C,
but prefer C over A, -
4:02 - 4:04this method fails to select a winner.
-
4:04 - 4:08Over the decades, researchers
and statisticians have come up with -
4:08 - 4:12dozens of intricate ways
of conducting and counting votes, -
4:12 - 4:15and some have even been
put into practice. -
4:15 - 4:17But whichever one you choose,
-
4:17 - 4:22it's possible to imagine it delivering
an unfair result. -
4:22 - 4:25It turns out that our intuitive concept
of fairness -
4:25 - 4:30actually contains a number of assumptions
that may contradict each other. -
4:30 - 4:34It doesn’t seem fair for some voters
to have more influence than others. -
4:34 - 4:38But nor does it seem fair to simply
ignore minority preferences, -
4:38 - 4:41or encourage people to game the system.
-
4:41 - 4:45In fact, mathematical proofs
have shown that for any election -
4:45 - 4:47with more than two options,
-
4:47 - 4:51it’s impossible to design a voting system
that doesn’t violate -
4:51 - 4:56at least some theoretically
desirable criteria. -
4:56 - 5:00So while we often think of democracy
as a simple matter of counting votes, -
5:00 - 5:05it’s also worth considering who benefits
from the different ways of counting them.
- Title:
- Which voting system is the best? - Alex Gendler
- Speaker:
- Alex Gendler
- Description:
-
View full lesson: https://ed.ted.com/lessons/which-voting-system-is-the-best-alex-gendler
Imagine we want to build a new space port at one of four recently settled Martian bases, and are holding a vote to choose its location. Of the 100 colonists on Mars, 42 live on West Base, 26 on North Base, 15 on South Base, and 17 on East Base. Assuming that everyone wants the port to be closest to their home base, what is the fairest way to conduct the vote? Alex Gendler digs into voting systems.
Lesson by Alex Gendler, directed by Biljana Labovic.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 05:08
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