Updating a Complex Mental Model—An Applied Election Odds Example

There are prob­a­bil­ities, and there are prob­a­bil­ities about prob­a­bil­ities. How do these get up­dated? I’ve had the same dis­cus­sion sev­eral times, and have tried to de­scribe this, but it is hard with­out go­ing into the math. The for­mal model is clear, but I have found that the prac­ti­cal im­pli­ca­tions are hard to de­scribe con­cretely. I just ran into a great con­crete ex­am­ple, how­ever, and I wanted to work through the logic of how I’m up­dat­ing as a way to show what should hap­pen.

The ex­am­ple I’m us­ing is my ex­pec­ta­tions about the 2020 elec­tion, how ac­cu­rate var­i­ous mod­els are, and how im­por­tant the in­puts are. This type of prob­lem is fairly com­mon—I have both an ob­ject level pre­dic­tion about the win­ner, and a pre­dic­tion about /​ model of how ac­cu­rate differ­ent sources of in­for­ma­tion will be.

So, what do I do when in­for­ma­tion comes in that seems sur­pris­ing? Two things; I up­date in the di­rec­tion the in­for­ma­tion in­di­cates, and I up­date against the re­li­a­bil­ity of the data. The sec­ond may seem counter-in­tu­itive, but the ex­am­ple makes it clearer.

The econ­omy is do­ing well—re­cent news is that it’s bet­ter than ex­pected. Pres­i­dents with great economies tend to get re-elected. Trump is also un­pop­u­lar. Un­pop­u­lar pres­i­dents tend not to get re-elected. How do we bal­ance these two, and how do they in­ter­act? My model of whether he will win is fairly un­cer­tain, and my model of the sources of data is also un­cer­tain. They are also re­lated in com­plex ways. For in­stance, if Trump’s pop­u­lar­ity plum­mets be­cause, for in­stance, the im­peach­ment in­quiries find some­thing shock­ing and hor­rible even to his base, I ex­pect that GDP mat­ters far less for his re­elec­tion chances. Other data sources also con­strain how far I will up­date—no level of GDP growth alone will make me say he’s cer­tain to win.

So I up­dated to­wards Trump’s re­elec­tion based on the eco­nomic data, but my un­der­ly­ing model is tel­ling me that it is de­creas­ingly rele­vant. That means I’m very slightly down-weight­ing the im­por­tance of eco­nomic fac­tors com­pared to ap­proval rat­ing, since he’s seem­ingly not get­ting credit for the growth (or the growth isn’t helping most vot­ers.) The net im­pact is that I have up­dated slightly to­wards Trump’s re­elec­tion.


1) For long term fore­casts of pres­i­den­tial elec­tions, fore­casts based on fun­da­men­tals do just OK. But fore­casts based on polls do poorly far in ad­vance of the elec­tion as well. (Spe­cial elec­tions seem to point to a huge shift to­wards the democrats, de­spite fun­da­men­tals.) More com­plete mod­els take some of each type of in­for­ma­tion—but how to com­bine them is tricky. Some mod­els do it poorly, oth­ers do it well.

2) I also have ex­pec­ta­tions about the fu­ture in­puts to the mod­els. Most pres­i­dents have fluc­tu­at­ing ap­proval rat­ings, so long-term fore­casts do poorly. For Trump, his split of ap­proval/​dis­ap­proval has been re­mark­ably steady, so un­less his ap­proval sig­nifi­cantly shifts from the cur­rent low-40s, or he runs against an in­cred­ibly un­pop­u­lar demo­crat (which is pos­si­ble, but seems pretty un­likely,) mod­els that con­sider this point to­wards him be­ing un­likely to win. It still may be volatile. For ex­am­ple, the im­peach­ment could solid­ify his base, or could re­duce his pop­u­lar­ity fur­ther.

3) This is tricky to de­scribe, but for un­der­stand­ing the over­all be­hav­ior, a use­ful strat­egy is to con­sider the limit—what hap­pens if the econ­omy is amaz­ing, but ev­ery­one hates the pres­i­dent? I’d as­sume he doesn’t get re­elected. Similarly, if ev­ery­one loves the pres­i­dent, but the econ­omy is in a deep re­ces­sion, (for which he’s seem­ingly not be­ing blamed) he prob­a­bly gets re­elected.

4) Spe­cial elec­tions are fa­vor­ing Democrats, voter turnout among liber­als is ex­pected to be very high be­cause of po­lariza­tion, etc.

5) By which I mean highly con­fi­dent—cer­tainty is im­pos­si­ble. It would take a con­fluence of events to make my highly con­fi­dent. Even with such a con­fluence of events, how­ever, it is far in ad­vance, so I’m not will­ing to put odds above ~90% /​ be­low ~10% be­cause I think there are fun­da­men­tally hard ques­tions about the fu­ture that im­pact the prob­a­bil­ity. (We don’t know who the demo­cratic nom­i­nee is, for in­stance.)