Portugal Elections: Results and alternative systems

Last January's Portuguese elections were interesting on two accounts: a) the Socialist Party won an outright majority against all odds; and b) it did so with an exceptionally high concentration of seats per vote. While I don't dismiss the importance of the first one, people more capable than me have already discussed it at length. So, I wanted to concentrate on the second one for a change.

A bit of background: Portuguese legislative elections have electoral circles at the district level, the most important first-level administrative subdivisions in continental Portugal. On top of that, there are also 4 other circles: the Azores, Madeira (both autonomous regions), the European, and the Outside of Europe circles. The number of seats assigned to each district (and region) depends on its magnitude (population-wise). The European and Outside of Europe circles elect a fixed number of 2 MPs each. District MPs are elected using a proportional system, namely the d'Hondt method. The d'Hondt method makes for a higher effective threshold than other allocation methods such as the Hare quota or Sainte-Laguë method, which are more generous to small parties.

Before these elections, the rule of thumb is that a party would require around 45% of the votes to get an outright majority. That rule broke down this year. Below I'm presenting the vote share, the number of seats, and seats' share of the largest party in all elections since 1991. I excluded elections where the largest party had less than 40% of the vote share. 

	Government	Vote Share	Seats		Seats (%)/ Votes (%)
		(%)	#	(%)
	Cavaco (III)	50.6	135	58.7	1.16
	Guterres (I)	43.8	112	48.7	1.11
	Guterres (II)	44.1	115	50.0	1.13
	Sócrates (I)	45.0	121	52.6	1.17
	Costa (III)	41.5	119	51.7	1.25

The last column is the ratio between both shares. In a perfectly proportional system, this would be close to one. PS only got 41.5% of the vote in this election (the lowest in the table) but gained 51.7% of all seats (the median value in the table). This gives a ratio of 1.25, the largest in all elections since 1991.

Out of curiosity, I decided to forecast the seats assigned to each party using significantly more proportional methods (only showing the parties that would have seats assigned by any of the methods). The first column is the number of seats each party would get under the technique. The second column would be the ratio between the seats and votes shares. And the third column would be the change relative to the d'Hondt method, our current standard.

Besides the Sainte-Laguë method, I also calculated using a genuinely proportional system by district and a proportional system using just one circle (i.e., assigning seats based on the total votes received).

	Party	d'Hondt		Sainte-Laguë			Proportional (District)			Proportional  (one circle)
	PS	119	1.25	107	1.12	-12	101	1.06	-18	98	1.03	-21
	PSD	78	1.16	74	1.10	-4	72	1.07	-6	69	1.03	-9
	Chega	12	0.72	15	0.90	3	21	1.25	9	17	1.02	5
	IL	8	0.71	10	0.89	2	10	0.89	2	12	1.07	4
	CDU	6	0.59	9	0.89	3	11	1.08	5	10	0.98	4
	BE	5	0.51	9	0.91	4	9	0.91	4	11	1.11	6
	CDS-PP	0	0.00	2	0.53	2	2	0.53	2	4	1.06	4
	PAN	1	0.27	2	0.54	1	2	0.54	1	4	1.09	3
	Livre	1	0.34	1	0.34	0	2	0.67	1	3	1.01	2
	RIR	0	…	0	…	0	0	…	0	1	1.01	1
	JPP	0	…	1	2.29	1	0	…	0	1	2.29	1
	Total	230		230			230			230

After every election, we hear about the need to change our system to a more proportional one. Right now, the debate surrounds uninominal circles (i.e., having a certain amount of circles, say 80, each with an equal number of population that elects one single MP), combined with a national circle. Another hypothesis would be to maintain the current method and then add a compensation circle, where votes that didn't elect any MP could be combined and then redistribute a certain amount of seats using those votes.

More proportional systems bring more representation, but it can hinder governability, as shown above. It can also give a more prominent voice to smaller parties. Whether that's good or bad will likely depend on the reader's political leanings.