As discussed previously, Chile has changed its electoral system for assembly elections (and for senate). The seat product (mean district magnitude times assembly size) was increased substantially. Now that the 2017 Chilean election results are in, did the result come close to the Seat Product Model (SPM) predictions?
The old seat product was 240 (2 x 120). The new seat product is 852.5 (5.5 x 155). This should yield a substantially more fragmented assembly, according to the SPM (see Votes from Seats for details).
I will use the effective number of parties (seats and votes) based on alliances. The reason for this choice is that it is a list PR system, and the electoral system works on the lists, taking their votes in each district and determining each list’s seats. Lists are open, and typically presented by preelection alliances, and the candidates on a list typically come from different parties. But the question of which parties win the seats is entirely a matter of the intralist distribution of preference votes (the lists are open), and not an effect of the electoral system’s operation on the entities that it actually processes through seatallocations formula–the lists. However, I will include the calculation by suballiance parties, too, for comparison purposes. [Click here for an important correction on the intralist allocation. Nonetheless, the error in the above does not affect any of the calculations in this post.]
The predicted values with the new system, for effective number of seatwinning lists (N_{S}) and effective number of voteearning lists (N_{V}), given a seat product of 825.5, are:
N_{S}=3.08 (SPM, new system)
N_{V}=3.45 (SPM, new system).
The actual result, by alliance lists, was:
N_{S}=3.09
N_{V}=4.02.
So the Chamber of Deputies is almost exactly as fragmented as the SPM predicts! In the very first election under the new system! The voting result is somewhat more fragmented than expected, but not wide of the mark (about 14%). It is not too surprising that the votes are more off the prediction than the seats; voters have no experience with the new system to draw on. However, the electoral system resulted in an assembly party system (or more accurately, alliance system) fully consisted with its expected “mechanical” effect. The SPM for N_{S} is derived from the constraints of the number of seats in the average district and the total number of seats, whereas the SPM for N_{V} makes a potentially hazardous assumption about how many “pertinent” losers will win substantial votes. We can hardly ask for better adjustment to new rules than what we get in the N_{S} result! (And really, that N_{V }result is not too shabby, either.)
Now, if we go by suballiance parties, the system seems utterly fragmented. We get N_{S}=7.59 and N_{V}=10.60. These results really are meaningless, however, from the standpoint of assessing how the electoral system constrains outcomes. These numbers should be used only if we are specifically interested in the behavior of parties within alliances, but not for more typical interparty (interlist) electoralsystem analysis. It is a list system, so in systems where lists and “parties” are not the same thing, it is important to use the former.
To put this in context, we should compare the results under the former system. First of all, what was expected from the former system?
N_{S}=2.49 (SPM, old system)
N_{V}=2.90 (SPM, old system).
Here is the table of results, for which I include Np, the effective number of presidential candidates, as well as N_{V} and Ns on both alliance lists and suballiance parties.

By alliance 

By sublist party 
year 
N_{S} 
N_{V} 
N_{P} 
N_{S} (sub) 
N_{V} (sub) 
1993 
1.95 
2.24 
2.47 
4.86 
6.55 
1997 
2.06 
2.54 
2.47 
5.02 
6.95 
2001 
2.03 
2.33 
2.19 
5.94 
6.57 
2005 
2.02 
2.36 
3.01 
5.59 
6.58 
2009 
2.17 
2.56 
3.07 
5.65 
7.32 
mean 
2.05 
2.41 
2.64 
5.41 
6.79 
We see that the old party (alliance) system was really much more defragmented than it should have been, given the electoral system. The party and alliance leaders, and the voters, seem to have enjoyed their newfound relative lack of mechanical constraints in 2017!
Can the SPM also predict N_{P}? In Votes from Seats, we claim that it can. We offer a model that extends form N_{V }to N_{P}; given that we also claim to be able to predict N_{V} from the seat product (and show that this is possible on a wide range of elections), then we can also connect N_{P} to the seat product. We offer this prediction of N_{P} from the seat product as a counterweight to standard “coattails” arguments that assume presidential candidacies shape assembly fragmentation. Our argument is the reverse: assembly voting, and the electoral system that indirectly constraints it, shapes presidential fragmentation.
There are two caveats, however. The first is that N_{P} is far removed from, and least constrained by, assembly electoral systems, so the fit is not expected to be great (and is not). Second, we saw above that N_{V} in this first Chilean election under the new rules was itself more distant from the prediction than N_{S} was.
Under the old system, we would have predicted Np=2.40, so the actual mean for 19932009 was not far off (2.64). Under the new system, the SPM predicts 2.62. In the first round election just held, N_{P}=4.17. That is a good deal more fragmented than expected, and we might not expect future elections to feature such a weak first candidate (37% of the vote). It is unusual to have N_{P}>N_{V}, although in the book we show that Chile is one of the countries where it has happened a few times before. Even the less constraining electoral system did not end this unusual pattern, at least in 2017.
In fact, that the assembly electoral system resulted in the expected value of N_{S}, even though N_{P} was so high, is pretty good evidence that it was not coattails driving the assembly election. Otherwise, Ns should have overshot the prediction to some degree. Yet it did not.