Vote for MMP -- with spreadsheets!

There's two new widgets in the sidebar, which will stay there until after the Ontario election and referendum. One links to the advocacy site for the Mixed Member Proportional site, the other to the government information site on the MMP referendum.

Notwithstanding my advocacy for MMP, I do have a couple of reservations about it:

• That the minority or coalition governments which will inevitably result will give too much power to tiny parties with loony views (ie. as the governing party panders to them to retain power).
• Governments need to be stable, and able to act without always being overthrown by non-confidence motions.
  
• I question what seems to be a popular (if tacit) assumption, that having the proportions of the legislature reflect the popular vote is somehow magically "democratic", in a way that other relationships between electoral choice and parliamentary seats are not.
  

However, what I've read of the The Ontario Citizen's Assembly on Electoral Reform (PDF here) persuades me that they Assembly did its homework, and took into account concerns such as the above.

So: I am voting for Mixed Member Proportional Representation. I don't want to belabour points made elsewhere, but briefly, I support it because:

• I think it has been, and is, bad for democracy in this country when parties can obtain large legislative majorities based on a low percentage of the total vote.
• Even if my preferred candidate has no hope of getting elected locally, I can still have some influence by voting for my preferred party. In other words, my franchise still counts for something.
  
• It allows minority views a voice in the legislature. One specific upside of this for me is that the Green Party might get some seats. OTOH, the downside is that so might the Family Coalition Party. I'm willing to take that risk.
  

However, I think the official promotion and education on the MMP system has been poor. For one thing, the video on the official government website really doesn't explain the system very well. I could only find one example of how the system would work, and it's both vague and confusing. Also, it's not hard to think of pathological cases that would "break" the seat-allocation system as described. Perhaps it's just because I'm a numbers geek, but I really wanted to understand how the list seat allocation works, and see some examples using made-up (but reasonable) numbers.

How MMP works

I finally found what I was looking for, buried on page 144&ff of the report of The Ontario Citizen's Assembly on Electoral Reform. To save y'all the trouble, I'll do my best to summarize the scheme here, by way of presenting the spreadsheet I cobbled up to play with scenarios (for anyone who really wants to understand the proposed system, I recommend reading that whole chapter of the report).

Example 1: "Typical" election

	Ridings Won		Party Vote	Quota Calculation			Quota Seats	Final Legislature		Disproportion
Party	#	%	%	Included	Weight	Seats Avail		#	%
A	47	36.43%	39.14%	TRUE	3.91E-001	47	51.77	52	40.31%	1.17%
B	31	24.03%	29.26%	TRUE	2.93E-001	31	38.7	39	30.23%	0.97%
C	12	9.30%	17.96%	TRUE	1.80E-001	12	23.76	24	18.60%	0.64%
D	0	0.00%	7.14%	TRUE	7.14E-002	0	9.44	9	6.98%	-0.16%
E	0	0.00%	4.03%	TRUE	4.03E-002	0	5.33	5	3.88%	-0.15%
Other	0	0.00%	2.47%	FALSE	0.00E+000	0	0	0	0.00%	-2.47%
Check totals:	90	69.77%	100.00%	Quota=	7.56E-003	129	129	129	100.00%	5.57%

Example #1 is taken from page 157 of the Report, and is intended to reflect a fairly typical Ontario election. There are five parties designated A through E, plus "other" representing any additional parties. The inputs to the spreadsheet are in red; everything else is a calculated result.

First, there are 90 seats for local ridings (the "# Ridings Won" column), elected in a First-Past-The-Post manner, just as they are today. The second input column is "% Party Vote", and reflects the new addition to the ballot, where the voter selects her/his preferred party. Note: the "% Ridings Won" column only totals to 69.77%, as this represents % of the entire legislature (139 seats), not just the 90 riding seats. The "Check Totals" line is so I can check that I assigned exactly 90 seats, and 100% of the party vote (and also verifies the sanity of calculations made in other columns).

The fun part comes when you start allocating the 39 list seats to bring the final proportionality of the legislature closer to the proportions of the Party Vote. The proposed Ontario MMP system uses something called the Hare Formula, which begins by calculating a quantity called the "Quota". The formula says:

Quota = (# Included Party Votes Cast) / (# Included Riding Seats + # List Seats)

The "Included" qualifier requires some explanation, as some Party Votes and Riding Seats are excluded from the Hare calculation. A party is excluded if its Party Vote is less than 3% of the total votes cast (see the "Other" line in Example #1). IMHO, this is a good thing: it means that the truly loony fringe can't gum up the works. It also means that the minimum number of seats any party can have based on Party Vote alone is three. (I'll deal with exclusion of Riding Seats in Example #2, below). In the table, which parties are included in the calculation is shown by TRUE or FALSE in the "Included" column. Parties which are included have their Party Votes carried over into the "Weight" column (since the readers of this blog -- all four of them -- are math/sci geeks, the use of scientific notation won't confuse anyone). The Report uses some made-up vote numbers for the Party Votes; for the spreadsheet I've just used the percentage (arithmetically, it works out to the same result). Similarly, the included Riding Seats are carried to the "Seats Avail" column. The "Quota" (given at bottom center) is then calculated by the Hare formula.

The number of seats each party should receive is then calculated as:

QuotaSeats = Quota * (Party Vote) / (Total Seats in Legislature)

Obviously, this usually yields some fractional seats. The official procedure for rounding these up or down to whole numbers is a bit complicated, and in the spreadsheet I've just used a simple a arithmetic rounding, which usually gets the same result (though in some cases it may magically create or abolish a seat). The 39 list seats are then distributed among the parties in order to bring their total representation up to the number given in the "# Final Legislature" column.

The result to pay attention to is the difference between the "% Party Vote" and "% Final Legislature" columns (calculated in the "Disproportion" column). The goal of MMP is to minimize the disproportion, and for many realistic election scenarios, it succeeds. In this example, the total disproportion (obtained by summing the absolute values of the per-party disproportions) is 5.57%.

Example #2: Overhanging Seats

	Ridings Won		Party Vote	Quota Calculation			Quota Seats	Final Legislature		Disproportion
Party	#	%	%	Included	Weight	Seats Avail		#	%
A	55	42.64%	39.14%	FALSE	0.00E+000	0	55	55	42.64%	3.50%
B	24	18.60%	29.26%	TRUE	2.93E-001	24	37.08	37	28.68%	-0.58%
C	11	8.53%	17.96%	TRUE	1.80E-001	11	22.76	23	17.83%	-0.13%
D	0	0.00%	7.14%	TRUE	7.14E-002	0	9.05	9	6.98%	-0.16%
E	0	0.00%	4.03%	TRUE	4.03E-002	0	5.11	5	3.88%	-0.15%
Other	0	0.00%	2.47%	FALSE	0.00E+000	0	0	0	0.00%	-2.47%
Check totals:	90	69.77%	100.00%	Quota=	7.89E-003	74	129	129	100.00%	6.

"Overhang" occurs when a party wins enough riding races to get a higher percentage of the legislature than the Party Vote would entitle them too. This is the other criterion by which a party will be excluded from the Hare Formula calculation, and receive no list seats. This is shown in the table above (taken from the second example in the Report). Here, Party A has won almost 43% of the seats in the legislature in the riding races alone, and 3.5% more than their share of the Party Vote. Thus, their seats are not included in the Quota Calculation (note that the total "Seats Avail" is thus only 74, ie. 129 minus 55). The final result is that A is slightly over-represented in Parliament, but not badly so.

Obviously, MMP means that majority government is the exception rather than the rule. The fun part here is to look at the results of these scenarios and speculate on likely alignments and coalitions (the magic number for legislative control being 65). Assume, say, that parties A, B, C and D are respectively Conservative, Liberal, NDP and Green (with E being possibly a religious or ethnic party) -- who gets to govern? Which parties are similar enough in philosophy to cooperate for three or four years?

Example 3: List Upset

	Ridings Won		Party Vote	Final Legislature		Disproportion
Party	#	%	%	#	%
A	50	38.76%	33.00%	50	38.76%	5.76%
B	30	23.26%	44.00%	53	41.09%	-2.91%
C	10	7.75%	19.00%	23	17.83%	-1.17%
D	0	0.00%	3.00%	3	2.33%	-0.67%
E	0	0.00%	1.00%	0	0.00%	-1.00%
Other	0	0.00%	0.00%	0	0.00%	0.00%
Check totals:	90	69.77%	100.00%	129	100.00%	11.52%

I played with a few more scenarios, just to see what happened. Example 3 shows a situation I call List Upset, in which party A wins a majority of the riding races, but B picks up enough list seats to achieve a plurality (and thus become the presumptive government). If this seems "wrong" to you, I suggest you are thinking about the MMP system the wrong way. You are stuck on the idea that the FPTP riding race is the "real" election, while the party vote is an illegitimate pretender which can be allowed only a secondary effect. In fact, this is exactly backwards: for good or ill, MMP is primarily a proportional representation system, but one that retains the concept of having a local representative.

And finally, an oddball example election I call Asymmetrical Landslide, in which A gets a legislative majority on riding seats alone, but B gets a majority of the Party Vote:

Example 4: Asymmetrical Landslide

	Ridings Won		Party Vote	Final Legislature		Disproportion
Party	#	%	%	#	%
A	70	54.26%	30.00%	70	54.26%	24.26%
B	13	10.08%	60.00%	50	38.76%	-21.24%
C	7	5.43%	5.00%	7	5.43%	0.43%
D	0	0.00%	3.00%	2	1.55%	-1.45%
E	0	0.00%	2.00%	0	0.00%	-2.00%
Other	0	0.00%	0.00%	0	0.00%	0.00%
Check totals:	90	69.77%	100.00%	129	100.00%	49.38%

The total disproportionality here is huge. However, I submit this is very unlikely to occur in a real election. It would require either that A won most of those ridings with only small pluralities, or that most voters decided to split their ballot, choosing the local candidate from A, but choosing B on the party vote.

So, the proposed MMP system is not my favorite alternative to FPTP, but I think it's a significant improvement. Should the referendum pass and MMP become law, we are in for interesting times in Ontario politics -- but hopefully in a good way.

Note: If I could figure out how to use Google Docs, I would post the spreadsheet there. However, being too lazy to do that, I'm willing to send a copy to anyone who asks. Just drop me a line (Open Office and Excel formats available).