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grime-dont-play
Guest
grime-dont-play

You guys are nerds

CH1CK3NS414D
Guest
CH1CK3NS414D

What I would have done off the bat is have each 1st choice count for 4 points, 2nd count for 3, etc., then just total the points

ChromeSabre
Guest
ChromeSabre

too much big brain, pepe win

billionispossible
Guest
billionispossible

Kinda geiy mod

EmoYogurt
Guest
EmoYogurt

69

unystormodimanzo
Guest
unystormodimanzo

Nice

LeFirecracker
Guest
LeFirecracker

I’m clicking all the links to see which one Rickrolls me

MagamangPrestige
Guest
MagamangPrestige

Pepe is the best! 👌

FriedCorn12
Guest
FriedCorn12

Thank you for the explanation

SavageSean33
Guest
SavageSean33

So I’m not asking this cuz I care about the winners, but as a statistics but, what makes Borda Count not up to snuff with ranked pairs?

SRIOUS_GAMER
Guest
SRIOUS_GAMER

Someone’s TRIGGERED

-Another_Redditor-
Guest
-Another_Redditor-

I read the whole thing man… It was actually pretty interesting.

__harsha__
Guest
__harsha__

This is big brain

rfrank54
Guest
rfrank54

Pepe FTW Regardless

xolyon
Guest
xolyon

Hmmmm (doesn’t understand any of it)

memegorl
Guest
memegorl

Thank you Dice, very cool

Jackg3904
Guest
Jackg3904

Gae

Jackg3904
Guest
Jackg3904

I’m green now

acetheboss111
Guest
acetheboss111

Still think Robbie Rotten is #1

153rick239
Guest
153rick239

somebody plz post a valid link

George0320
Guest
George0320

Spongebob and Pepe would both be acceptable as MOTD for me

Hydroplane2010
Guest
Hydroplane2010

That’s pretty gay

GamationOnReddit
Guest
GamationOnReddit

my brain is too small to understand this so i’m gonna assume you’re right

i_am_ARTISTIC
Guest
i_am_ARTISTIC

what the hecc kind of youtub conspiracy theory

caveman5467
Guest
caveman5467

I would have been happy with spongebob aswell, but I’m glad Pepe won

Wemmbo
Guest
Wemmbo

Glad that pee pee won

hercs247
Guest
hercs247

Data graphs available [right here](https://youtu.be/oHg5SJYRHA0) and also in this [Dropbox ](https://youtu.be/oHg5SJYRHA0)

-spartacus-
Guest
-spartacus-

Maybe I missed this answer, but why not do the point system of 4 points for your first vote, 3 points for second, 2 for 3rd, and 1 for forth?

xolyon
Guest
xolyon

F in the chat to all those who lost – you will still forever be numba one

yoLeaveMeAlone
Guest
yoLeaveMeAlone

While I personally believe SpongeBob should have won, I will recognize Pepe’s victory, and offer a [song of tribute](https://youtu.be/k9iYm9PEAHg)

dicemaze
Guest
dicemaze

Did Pepe really win the MOTD vote?

In short answer, yes. In long answer, uh, it depends on how you count the votes. In some ways, Spongebob kinda won. In another way, no one won. However, in most ways, Pepe won. If you’re interested in how this works out, please read the write-up below.

In addition, at the bottom of this write-up, I have linked an Excel sheet with the **full vote results/data set** for maximum transparency.

———————————————

I’m /u/dicemaze, a current Mathematics major, and I’m here to give you, the users of r/dankmemes, the rundown on the surprisingly nitty-gritty math behind the final MOTD vote. **There is a TL;DR at the bottom if you wish to just jump there.**

Okay, so to start, we promised y’all a ranked voting system, and we held true to that. The final result with Pepe the Frog winning is the outcome of analyzing your votes used a [Ranked Pairs](https://en.wikipedia.org/wiki/Ranked_pairs) voting system, a powerful and thorough method of determining the winner of any ranked vote. However, this was not the first method we looked at. First, we tried the method of…

#INSTANT RUN-OFF VOTING

[Instant Run-off Voting](https://en.wikipedia.org/wiki/Instant-runoff_voting) or IRV, was the first candidate for our analysis. We initially chose this because our head mod was familiar with the method, and it was suggested to us by a couple of users that follow our [Twitter](https://twitter.com/dankmemesreddit). IRV looks to see if there is a majority of people who chose a given candidate as their #1 choice, and if there is, a winner is declared. Easy. If there isn’t, it eliminates the least popular candidate from the pool, and then redistributes those votes based on their second choice. After doing that, IRV looks again to see if there is a majority. If there isn’t, it repeats the process again, eliminating the next least popular candidate, and transferring votes over to people’s second or third favorite choices. It continues doing this until one candidate has a majority of votes.

So what does this look like for our MOTD data? Well, it looks like this:

|Initial counts based on first choice:| |
:–|–:|
|16378|Pepe|
|11719|Spongebob|
|12562|Rick Roll|
|8918|Tom & Jerry|
|||
|First round loser:|Tom & Jerry|
|||
|New totals:||
|18058|Pepe|
|16771|Spongebob|
|14748|Rick Roll|
|||
|Second round loser:|Rick Roll|
|||
|New Totals:||
|24624|Pepe|
|24953|Spongebob|
|||
|Winner|Spongebob|
|||
|Difference|329|
|Percent difference|0.66%|
As you can see, from the initial data, it looks like Pepe should be a shoe-in to win. He has significantly more first choice votes than anyone else, almost 4k more votes than RickRoll’d, the second-place meme. However, there is no majority, so IRV does its thing and eliminates Tom and Jerry, the losing meme. T&J’s votes get redistributed based on their second choices, and, surprise surprise, Pepe is still winning, and but still not with a majority. IRV does its thing again, eliminates Rick, and surprisingly comes up with *SpongeBob* as our winner for MOTD.

You might think, OK, so Spongebob should be the winner, right? Well, not exactly. If you look back at the initial set of data, Spongebob is in *third*. That’s right, next to last. It goes Pepe > Rick > SB > T&J. Plus, if you look at the margin, SB *barely* wins under IRV. In both the first and second rounds, Pepe wins by at least a thousand votes; in the last round Spongebob wins by just 329, only 0.66% of the total number of votes. With a vote that close despite there being 24 possible ways to arrange the 4 candidates, any statistical test you run will show you that the results of this vote are not statistically significant, i.e. no true winner can be decided via this method

What’s more, /u/ELFAHBEHT_SOOP and I dug around a little more about ranked-choice voting and discovered that IRV is not that great of a system, [it has a *lot* of flaws]( https://en.wikipedia.org/wiki/Instant-runoff_voting#Non-satisfied_criteria). In particular, it does not meet the Condorcet criterion. That’s just fancy math talk to say that IRV is not mathematically sound, and can sometimes lead to extreme and non-representative results. In fact, in some scenarios, such as ours, you can actually *hurt* your preferred candidate’s chances of winning by placing them first. How is this possible? Well, IRV actually ignores a lot of data. Say you put Pepe first. Since Pepe made it to the final round, it does not matter in which order your other three were stacked. You could have had SpongeBob second, or SpongeBob last. It doesn’t matter. Meanwhile, if you had placed Pepe third and SpongeBob last, IRV knows that you preferred all three candidates, including Pepe, over SpongeBob. So yeah, it turns out IRV kinda sucks, and the way it ignores info sheds a little light on how the meme initially in third place can suddenly be vaulted to first. So what to do now? Well, this leads us to the method of…

#RANKED PAIRS

This, unlike IRV, is a Condorcet complete method of determining a winner. In other words, it’s mathematically rigorous. In addition, it doesn’t ignore any data, unlike IRV. The way RP works, is that you arrange your candidates in head-to-head pairs (so in our case, we have 6 pairs), and we go through each submission and write who wins in that submission for that pair. Then, you tally up all the results and look at the overall winner in each head-to-head matchup. After that, you create a graph with an arrow going from the winners to the losers of each matchup. Whatever candidate is the source of the graph, wins. There are safeguards in RP in case you have ties or scenarios with cycles (i.e. Pepe beats Tom, Tom beats Spongebob, and Spongebob beats Pepe), but thankfully we didn’t have that in our case. The data for our MOTD vote under RP is shown below:

|Ranked Pairs|
:–|
|1. SB beats TJ in 6617 more submissions than TJ beats SB|
|2. SB beats RICK in 3915 more submissions than RICK beats SB|
|3. PEPE beats RICK in 3895 more submissions than RICK beats PEPE|
|4. PEPE beats SB in 3149 more submissions than SB beats RICK|
|5. PEPE beats TJ in 3147 more submissions than TJ beats PEPE|
|6. RICK beats TJ in 111 more submissions than TJ beats RICK|

The graph looks like [this]comment image). As you can see, Pepe is the source of the graph, which means it is the winner. What the graph is saying is that Pepe wins in every head-to-head matchup with the other candidates. This means that if we made a bracket between the final four memes, **no matter how we made it**, Pepe will always win. Plus, since RP is Condorcet complete, some fancy Graph Theory result says that **any other** Condorcet complete method used to analyze our data set will arrive at the same result. In fact, Pepe is what we call the Condorcet Winner of our data set.

Even though at this point we were confidant in our winner, I also wanted to briefly look at one more ranked voting system. This was the first ranked-voting system that came to my mind, and was something that I had wanted to try out since we had first said we were going to do a ranked-voting system for the final four.

#BORDA COUNT

In this system, each meme is awarded points for each vote submission based on its ranking. Every time a meme is voted as someone’s first choice, it gets a whole point; every time it is voted second choice, it gets half a point; third choice gets a third of a point, and fourth choice gets a fourth of a point.

Borda Count has its ups and downs. Like RP, it doesn’t ignore any data, but isn’t Condorcet complete. However, unlike IRV, it’s impossible to hurt your favorite candidate’s chances of winning by putting them first. In this way, you can think of it as a method in between RP and IRV. If you tally up these votes, you get the following data:

|Pepe|SpongeBob|Rick|Tom|
:–|–:|–:|–:|
|27806.01|26128.11|25427.74|23758.3|
Again, Pepe wins with more than a thousand more points over second place. It’s a simple system that is both easy to visualize and easier to run than IRV or RP, but we still feel that RP is the definitive system for these kinds of votes.

#CONCLUSION

So yeah, that’s it! All in all, we feel the most comfortable stating that Pepe is your Meme of the Decade! Not only is the Condorcet Winner of this data set by winning via Ranked-Pairs (the most mathematically rigorous system of the ones we looked at), but it also wins the Borda Count system and has the most number of first place votes. However, if you really loved SpongeBob, maybe you can take some comfort in knowing that there is a ranked-choice voting system out there that has it winning.

If you want to see the full data set, you can find it [here](https://drive.google.com/file/d/1y1pVEWoOtk-F8ZHeoAz0mIV2DsfONeyf/view?usp=sharing). However, be aware that this excel file is *huge* and will probably cause your browser or Google Sheets app to lag and/or crash.

If you want to go even more in-depth into ranked-choice voting or the Condorcet Criterion, [this](https://www.youtube.com/watch?v=dQw4w9WgXcQ) is a good, free resource from Princeton University that /u/ELFAHBEHT_SOOP and I used throughout this whole process.

#TL;DR

**Pepe both has the most number of first place votes *and* wins in the strongest/most mathematically rigorous ranked-choice voting system, but there is another popular-but-flawed system in which SpongeBob wins.**

^also ^happy ^bday ^to ^/u/kesha_paul ^we ^love ^you ^and ^you ^keep ^us ^in ^check ^<3

Rusty1885
Guest
Rusty1885

mafs

meneldor_hs
Guest
meneldor_hs

Putting pepe as meme of the decade was the safest call. Otherwise this whole sub would rage how voting was rigged and I do agree with maths that you went with. I’m glad Spongebob memes stood so well against the symbol of the decade

IndianBroArmy
Guest
IndianBroArmy

I read the whole thing. Hope you’re happy.

ZanyFish
Guest
ZanyFish

Welcome back to MEME THEORY

Brommando007
Guest
Brommando007

Rick Rollers for life

OldKarrot
Guest
OldKarrot

Why would you do all this complicated stuff? I would just set it up so you have your four candidates, and you vote for your favorite. Whoever gets the most votes wins, seems more straightforward.

Ki_Andi_Mundi
Guest
Ki_Andi_Mundi

I appreciate the rigorous nature of deciding who the winner should be. Nice work lads and ladettes.

ThePhoenixKing601
Guest
ThePhoenixKing601

This is what the cultured among us would call a big brain moment. 🧠

Tyrannosaurus_Rox_
Guest
Tyrannosaurus_Rox_

What a great way of introducing people to alternative voting systems! Now I have a real-life example for demonstrating IRV and ranked pairs. Thank you for the work you’ve put into this