Vote Pairing is a Cost-Effective Political Intervention

Summary

Vote pairing is a prac­tice whereby in­di­vi­d­u­als agree to swap votes. Wikipe­dia sum­ma­rizes it as:

In United States pres­i­den­tial elec­tions, vote pairing usu­ally comes in the form of vot­ers from “safe” states, or non-swing states, vot­ing for third-party can­di­dates, and vot­ers from swing states vot­ing for their sec­ond-prefer­ence can­di­date. This form of vote pairing en­courages third-party sup­port while min­i­miz­ing the risk that the more fa­vored ma­jor-party can­di­date will lose elec­toral votes in the na­tion­wide elec­tion (i.e., the “spoiler effect”). In the 2016 United States pres­i­den­tial elec­tion, this has usu­ally man­i­fested in the form of sup­port­ers in swing states of Liber­tar­ian can­di­date Gary John­son and Green Party can­di­date Jill Stein swap­ping votes with sup­port­ers in blue states of Demo­cratic can­di­date Hillary Clin­ton.

The prac­tice’s le­gal­ity has been up­held by the Ninth Cir­cuit Court of Ap­peals, and large num­bers of swaps oc­curred dur­ing the 2000 and 2016 elec­tions.

Tens of thou­sands of peo­ple have par­ti­ci­pated in swaps, but I am not aware of any es­ti­mates of the cost effec­tive­ness of this prac­tice. This post pro­vides in­for­ma­tion on the cost effec­tive­ness, based on my work with a vote pairing web­site, Make Mine Count (MMC).

Note: for sim­plic­ity, this ar­ti­cle talks about how to in­crease the num­ber of votes to a ma­jor party can­di­date via vote pairing, but it does not con­sider the value of that in­crease. In 2016 vote pairing helped the Democrats, but I ex­pect that the effec­tive­ness should be similar if/​when the ta­bles are turned and vote pairing benefits Repub­li­cans.

Rather than talk­ing about “Can­di­date A” and “Can­di­date B” I use the names “Clin­ton” and “Trump”, but this ar­ti­cle should not be con­strued as ar­gu­ing whether Clin­ton or Trump was a bet­ter can­di­date.

Key Results

  • I per­son­ally av­er­aged ~10 swing state vot­ers per hour of work, which is 30 times more effec­tive than go­ing door to door.

  • I es­ti­mate that MMC in­creased Hillary Clin­ton’s chance of win­ning by about one in 210,000. (For com­par­i­son pur­poses, the av­er­age voter has a one in 60 mil­lion chance of chang­ing the elec­tion out­come.) If other vote pairing web­sites had similar suc­cess rates, in ag­gre­gate vote pairing in­creased Clin­ton’s chance of win­ning by one in 15,000.

  • The site over­all av­er­aged ~2 swing state vot­ers per hour of work, which is 6 times more effec­tive than go­ing door to door.

  • Vote pairing could plau­si­bly have changed the out­come of the 2000 US pres­i­den­tial elec­tion, if pairing had hap­pened in 2000 at the same rate that it hap­pened in 2016.

  • Vote pairing seems to be more cost-effec­tive than mak­ing calls, go­ing door to door, or other stan­dard forms of chang­ing elec­tion out­comes, pro­vided you are in the very spe­cial cir­cum­stances which make it effec­tive.

In this ar­ti­cle, I dis­cuss the benefits that MMC pro­vided, es­ti­mates of the cost, es­ti­mates of what my coun­ter­fac­tual im­pact was, and guidance on what we should have done bet­ter.

Overview of Make Mine Count

I be­came in­ter­ested in vote trad­ing sev­eral months be­fore the 2016 US pres­i­den­tial elec­tion. At the time there were two ma­jor vote pairing plat­forms: Make Mine Count and #Nev­erTrump.2 I vol­un­teered my time over a cou­ple months to make im­prove­ments to the MMC plat­form.

The plat­form worked as fol­lows: users would sign up, list­ing their state and can­di­date prefer­ence. Clin­ton vot­ers in safe states would be paired with third-party vot­ers in swing states, and they would be con­nected through a se­cure, pri­vate mes­sag­ing sys­tem. After be­ing con­nected, they would mes­sage each other to en­sure that both wanted to be paired, af­ter which they would each vote for the other’s can­di­date.

Results

Out of the 2319 peo­ple who cre­ated an ac­count, 610 were matched and I es­ti­mate that a to­tal of 132 votes were cast for Clin­ton in swing states.

This breaks down as fol­lows:

  • 2,319 users cre­ated an account

  • Of these, 153 were Clin­ton vot­ers in swing states and 507 were non-Clin­ton vot­ers in safe states, mak­ing them in­el­i­gible to be paired. This leaves 1,659 users who were el­i­gible for a match.

  • Of these, 600 were matched. This was due to a sur­plus of Clin­ton vot­ers in safe states (more on this later)

  • Of that 600, 472 sent or re­ceived at least one mes­sage, and 362 sent and re­ceived one mes­sage. Pre­sum­ably some frac­tion of peo­ple who didn’t mes­sage each other still went through with the swap (e.g. be­cause they called each other in­stead of us­ing the mes­sag­ing fea­ture), but I think this is small and will as­sume that only these 362 con­sid­ered hav­ing a swap.

  • From a ran­dom sam­pling of 100 anonymized mes­sages, ap­prox­i­mately 86% of peo­ple who signed up were in­ter­ested in ac­tu­ally go­ing through with the swap. Most of the 14% who signed up but did not want to use the plat­form were peo­ple who had signed up but for­got­ten about it, and early voted, mak­ing them in­el­i­gible to swap. In my sam­ple of 100, there were also 2 peo­ple who did not seem to un­der­stand the plat­form (they used it to try to con­vince their match to vote for Jill Stein in­stead of swap­ping) and 1 per­son who was a Trump troll (promised to swap but re­neged). There were also a few who signed up as third-party sup­port­ers, but de­cided to vote for Clin­ton.

  • A swap needs both par­ties to be in­ter­ested, and there­fore .862 = 73% of matches re­sulted in a swap.

  • This leaves us with an es­ti­mated 264 le­gi­t­i­mate swaps, of which half were votes for Clin­ton, i.e. 132 votes for Clin­ton in a swing state were cast as a re­sult of the MMC plat­form.

Ad­di­tion­ally, be­cause MMC had a sur­plus of Clin­ton vot­ers, we sent these vot­ers a recom­men­da­tion to use a differ­ent site (Trump Traders (TT)) which had a sur­plus of third-party vot­ers. 75 of these users made a TT ac­count and, since these users were highly mo­ti­vated, a large frac­tion of them pre­sum­ably went through with a swap, but I do not have ac­cess to that data. [TT did not re­turn my re­quest to share data for this ar­ti­cle.]

Im­pact Analysis

Be­cause of the nu­ances of the Elec­toral Col­lege, votes in some states are much more likely to swing the elec­tion than oth­ers. FiveThir­tyEight com­piled a “voter power in­dex” (VPI), which com­pares the rel­a­tive power of the vote. A VPI of 1 means that a voter in that state has an av­er­age chance of swing­ing the elec­tion (~1 in 60 mil­lion). A VPI of 2 means that a voter in that state has twice the av­er­age chance (~2 in 60 mil­lion) etc.

The VPI of each state fluc­tu­ated through­out the cam­paign, and for sim­plic­ity I used the most re­cent num­bers (calcu­lated Novem­ber 7, 2016). Ob­vi­ously, vote pairing is more valuable when the cam­paign is close and less valuable when it’s a sure thing, so de­pend­ing on which num­bers you use and when you calcu­lated those num­bers, you will get differ­ent es­ti­mated im­pacts. I also as­sumed in­de­pen­dence (i.e. one voter with a VPI of 2 is as good as two vot­ers with a VPI of 1) – this is slightly un­true, but I don’t think it makes a big differ­ence at the scales I am talk­ing about in this doc­u­ment.

State

Num­ber of Swapped Votes Through MMC

Effec­tive Votes (0.73 * Votes)

Voter Power In­dex3

Prob­a­bil­ity Of Chang­ing Out­come Of Elec­tion (VPI * EV)

GA

1

0.73

0.8

9.73E-09

WI

21

15.33

2.1

5.37E-07

PA

18

13.14

2.9

6.35E-07

MN

48

35.04

1.7

9.93E-07

AZ

16

11.68

1.5

2.92E-07

FL

7

5.11

2.5

2.13E-07

VA

7

5.11

2

1.70E-07

OH

21

15.33

1.2

3.07E-07

NH

1

0.73

4.3

5.23E-08

NV

3

2.19

4.5

1.64E-07

SC

2

1.46

0.2

4.87E-09

NM

1

0.73

4.8

5.84E-08

NC

17

12.41

3.2

6.62E-07

MI

6

4.38

3.2

2.34E-07

CO

12

8.76

2.9

4.23E-07

Total

181

132.13

2.52 (av­er­age)

4.75E-06

The to­tal im­pact was 4.7e-6 ~= one in 210,000. Another web­site (Trump Traders) ad­ver­tised 45,000 users but was only two-thirds as effec­tive on a per-user ba­sis as MMC.4 If they had suc­cess rates similar to ours, they would’ve in­fluenced Clin­ton’s chances by about one in 16,000.5 I was not able to find num­bers for #Nev­erTrump, but it seems plau­si­ble that all the sites com­bined in­creased Clin­ton’s odds by about one in 15,000.

Costs

  • Steve, the pri­mary de­vel­oper of MMC, es­ti­mates that he spent 40 hours writ­ing code and an ad­di­tional 40 hours think­ing about the site.

  • Steve spent $310 for host­ing and mis­cel­la­neous costs.

  • Two sep­a­rate groups bought ads for MMC for $500 each

  • I spent seven hours of my time work­ing on the MMC site.

The to­tal cost was 50-90 hours of la­bor plus $1,310 in hard costs.

Coun­ter­fac­tual impact

It seems un­likely that very many peo­ple would have paired with some­one on their own, with­out a vote pairing site ex­ist­ing. There­fore, the coun­ter­fac­tual is mostly about what frac­tion of these peo­ple would have oth­er­wise used a differ­ent site.

Coun­ter­fac­tu­als are always very hard, but we can cre­ate some bounds:

  • Of the ~800 un­matched Clin­ton vot­ers we emailed recom­mend­ing that they sign up for TT, 75 did. They would not have signed up for TT if they had already signed up for an­other site, so at least 10% of the votes were coun­ter­fac­tu­ally valid.

  • Of the 100 users I ex­am­ined, only one said that they had signed up for an­other site and were there­fore not go­ing through with the swap. This gives an up­per bound of 99%.

My guess is that it’s more to­wards the up­per side (10% is a very high click through rate for any email).

Per­sonal Coun­ter­fac­tual Impact

“I am not a mem­ber of any or­ga­nized party – I am a Demo­crat” – Will Rogers

One gen­eral prob­lem I found is that peo­ple wanted to cre­ate their own vote pairing web­sites in­stead of work­ing to­gether – this is ob­vi­ously in­effi­cient due to the net­work effects re­quired for vote pairing to work, but I wasn’t able to make that ar­gu­ment suc­cess­fully.

There were 4 vote pairing web­sites I had some con­tact with, but the only time I was ever able to suc­cess­fully con­vince peo­ple to not du­pli­cate work was when I sent some of our (MMC) users to a differ­ent site. (No one seemed in­ter­ested in “shar­ing” in the true sense of the word. Nei­ther Trump Traders nor #Nev­erTrump re­sponded to my re­quest to share data for this ar­ti­cle, for ex­am­ple.)

In terms of things I per­son­ally can claim credit for:

  1. Created Face­book in­te­gra­tion for the site, and some gen­eral site clean­li­ness stuff (e.g. the so­cial me­dia “share” but­tons did not work when I first started). 36 votes were us­ing Face­book in­te­gra­tion, and Face­book was the vast ma­jor­ity of our user traf­fic (70%). I will give my­self 25% of the 132 MMC Clin­ton votes for this (= 33 Clin­ton swing state votes).

  2. Co­or­di­nated refer­ring vot­ers from MMC to TT. It seems ex­tremely un­likely to me that any­one else would’ve done this if I had not, and there­fore I will give my­self all of the 75 referred peo­ple (= 37 Clin­ton swing state votes [TT paired 2 Clin­ton vot­ers with ev­ery third-party voter]).

  3. I posted on my Face­book, which got 3 ac­counts in TT (= 2 Clin­ton swing state votes)

This im­plies that I got 72 Clin­ton votes with my 7 hours of work. This is in­cred­ibly high – 20-30 times higher than “tra­di­tional” out­reach like go­ing door-to-door (which I also did).6

Note that al­most all of this im­pact is due to the fact that I was will­ing to join some­one else’s pro­ject in­stead of start­ing my own. Start­ing a new vote pairing web­site is in­her­ently much less cost-effec­tive be­cause of the setup costs and time and the fact that it is split­ting apart the voter pool, mak­ing it more difficult for peo­ple to be matched.

Linchuan’s impact

As an ex­am­ple of what a small amount of highly tar­geted ad­ver­tis­ing can do, Linchuan Zhang posted on his Face­book that Trump Traders needed more Clin­ton vot­ers, and that one post re­sulted in 24 TT ac­counts (= 12 Clin­ton swing state votes). It prob­a­bly took him less than 15 min­utes to write this post, which means that it was about 100 times as pro­duc­tive as go­ing door-to-door.

Things to do differently

  1. There was a ton of un­nec­es­sary and du­pli­cated work be­cause so many peo­ple de­cided to cre­ate their own prod­ucts in­stead of work­ing to­gether. I’m not sure how to solve this.

  2. We de­cided to wait un­til close to the elec­tion in or­der to match peo­ple up so that we could ac­cu­rately de­ter­mine which states were “in play”. This re­sulted in a lot of peo­ple for­get­ting that they had signed up (or as­sum­ing the site didn’t work). We should have had more fre­quent touch points, or matched peo­ple sooner.

  3. Many peo­ple seem to be con­cerned about fraud (i.e. some­one would promise to trade with them but would se­cretly vote for Trump). This isn’t a very le­gi­t­i­mate con­cern – the en­tire premise of vote pairing is that Clin­ton votes in blue states are worth­less, so Trump ad­vo­cates would have noth­ing to gain by do­ing this7 – but I would guess that it turned a sig­nifi­cant num­ber of peo­ple off the idea. We should have done a bet­ter job of coun­ter­ing this claim.

  4. I did not in­vest very much time into pro­mot­ing the site, largely be­cause I was un­clear about how effec­tive it would be. I think I prob­a­bly could have got­ten on lo­cal news or other me­dia if I had re­ally tried. For­tu­nately, now that this doc­u­ment ex­ists (and if it’s shared widely), peo­ple work­ing on vote pairing in 2020 will bet­ter un­der­stand its effec­tive­ness.

Summary

In the 2000 pres­i­den­tial elec­tion, Gore lost Florida by 537 votes. More than 5000 votes were swapped in Florida alone in the 2016 elec­tion,8 in­di­cat­ing that the out­come of the 2000 pres­i­den­tial elec­tion could rea­son­ably have been changed if vote pairing hap­pened in 2000 at the same rate that it hap­pened in 2016.

Vote pairing seems to “punch above its weight” in terms of effec­tive­ness, but will only be use­ful when there are large num­bers of peo­ple who want to vote for a third-party can­di­date. Fur­ther­more, cre­at­ing a new vote pairing site from scratch is likely to be much less effec­tive than the num­bers listed here, and is pos­si­bly less effec­tive than tra­di­tional GOTV ac­tivi­ties.

If the 2020 elec­tion is as high-stakes as the 2016 one, and I am similarly po­si­tioned to how I was in 2016, I will very likely work on voter pairing again.

Acknowledgments

I would like to thank Steve Hull for cre­at­ing MMC, open-sourc­ing it and shar­ing anonymized data; Linchuan Zhang for talk­ing about the elec­tion and vote pairing with me; the Trump Traders team for ac­cept­ing referred users and shar­ing con­ver­sion rates; Rob Wiblin, Gina Stuessy and Linchuan Zhang for read­ing drafts of this ar­ti­cle; and Rob Wiblin for the gen­eral mo­ti­va­tion for be­com­ing in­volved in the cam­paign.

Footnotes

  1. https://​​www.stat.berkeley.edu/​​~al­dous/​​157/​​Papers/​​vote.pdf

  2. Sev­eral other sites, like Balanced Re­bel­lion and VotePact ex­isted, but these were fo­cused on elect­ing third-party candidates

  3. The ob­ser­vant reader will note that some of these states have a VPI less than 1, which in­di­cates that they prob­a­bly should not have been swapped. We used Prince­ton Elec­tion Con­sor­tium data to de­ter­mine swing states which, in ret­ro­spect, was a bad idea. The in­ac­cu­racy of these fore­casts led to PEC’s cre­ator eat­ing a bug on live TV.

  4. They matched 2 Clin­ton vot­ers to one third party voter

  5. (45,000/​2,319)*(2/​3)/​(210,000)

  6. See this table from Get Out The Vote. I per­son­ally was able to con­tact many fewer peo­ple per hour than GOTV claims is av­er­age when go­ing door to door or call­ing peo­ple (mean­ing that vote pairing was even more cost-effec­tive in com­par­i­son).

  7. A Trump ad­vo­cate might be able to get some benefit by ly­ing, be­cause they would pre­vent a le­gi­t­i­mate pair from hap­pen­ing, but this is not a rea­son to not sign up be­cause the worst case sce­nario is ex­actly the same as the sce­nario un­der which you don’t sign up (i.e. the swap is wasted)

  8. https://​​www.face­book.com/​​trumptraders/​​pho­tos/​​a.750408771766492.1073741828.742762899197746/​​757681704372532/​​?type=3&the­ater