[Election-Methods] Measuring power in a multi winner election

[Howard Swerdfeger]

Juho wrote:
> Some random observations on the theme.
> 
> "Seats != power" seems to assume that there is a hard party discipline 
> (=all party representatives will/must vote as told by the party). Or 
> alternatively representatives could have different weights (different 
> number of votes each).
> 
> You skipped the "normal" rule of proportional systems where votes = 
> seats quite quickly. It has its problems but I guess also possible power 
> measurement based methods would have some problems. Let's say there is a 
> rule that one can modify the constitution with 75% of the votes. There 
> are three parties: 45%, 45% and 10%. Should we now give the smallest 
> party more power by allowing it to modify the constitution together with 
> one large party in some cases (with only 55% of the votes)?

I ran some number for New Zealand which went from FPTP to MMP several 
years ago.
indeed the NZ does have a much better proportional representation number 
since the change

1993 election was the last one under first past the post it had 
dis-proportionality index (Gallagher) of 18.28 but its dis-propotional 
power index in 1993 was 54.

The following shows the rise in propotional Rep, and Power as NZ moves 
to MMP

|---------|----------|------------|---------|
|  YEAR   | PropRep  | PropPower  | System  |
|---------|----------|------------|---------|
|  1993   |  18.3    |  54.0      |  FPTP   |
|  1996   |   6.0    |  10.2      |   MMP   |
|  1999   |   4.7    |  12.2      |   MMP   |
|  2002   |   3.9    |  24.2      |   MMP   |
|  2005   |   1.3    |  16.4      |   MMP   |
|---------|----------|------------|---------|

These numbers are with Gallagher proportionality Index and Banzhaf Power 
Index.
Similar trends are seen with Sainte-Laguë proportionality Index and 
Shapley-Shubik power index.


it becomes obvious that proportional representation increases (in 
general) Proportional power, but there is a much weaker relationship 
there (2002).


> 
> With 50% limit and parties 30%, 30%, 30%, 10%, should we allow minority 
> decisions in some cases to allow the small party to decide in some cases?
> 

True from the break down in the numbers small parties were often "Over 
valued" in there power index. I looked like this power may have come at 
the expense of the second party though not the first in many cases.
But this trend is less clear and I would need to run a LOT more numbers 
to see for sure.
Think Scotland, Germany, Italy, etc...

> One alternative approach would be to require higher percentage of votes 
> in some cases, e.g. after decisions have been made with lower 
> percentages for few times. In this case 30%+30% would not be enough any 
> more in some cases but the the approval limit would go up from 50% e.g. 
> to 65% at some point.

Good point, I ran my numbers with a threshold of 50% of the seats, 
rounded up.
the threshold could be altered, and it is unknown how this would effect 
the power index.
My guess would be that as the threshold was raised to 100% of the seats 
it would Slowly equalize the power between the parties.


> Note that if the parties will make majority decisions that then require 
> all the party representatives to vote as decided this means that some of 
> the party representatives may have to vote against their will. The party 
> is allowed to wield power but part of the representatives will wild the 
> power against themselves. The party has power but the representatives 
> and supporters would in some cases be hurt by this power (maybe the 
> alternative that lost had majority support among (all) the 
> representatives and voters). The party "won" but maybe not all of its 
> representatives and supporters.

yes, I was basing my assumptions on the Westminster model. which tends 
to create high degree of party discipline, especially in Canada (my home).

> 
> I guess the basic idea behind party discipline is that this way the 
> party is able to reach a better negotiation position. A party that is 
> internally split 50%-50% on some question can still do horse trading and 
> agree with some other party to support that party in this vote if that 
> party will support this this party in some future vote. The power of the 
> parties now follows the power measurement schemes instead of "votes = 
> power". But in principle parties that together have sufficient majority 
> may take a dictator role. It is hard to design systems that would 
> eliminate the possibility of this kind of party negotiation level voting 
> discipline (if one party can do this, why not a group of parties too).
> 
> Voting methods that would take the power measurement aspects into 
> account may give more power to the small parties in order to allow them 
> to decide more than they would otherwise be allowed to. This could lead 
> to a strategic for the big parties to split at least formally but still 
> after the elections use strong party discipline that would now cover all 
> the party fragments.

agreed, perhaps a system that takes "Power" into account as a secondary 
measure. would be appropriate.

thinking of the top of my head : a kind of double top up like MMP
with
X reserved Local Seats
Y reserved proportional representation Top up Seats
Z reserved proportional Power top up seats

Where usually
X > Y > Z

and seats are allocated in that order.


> How about using the more traditional votes = seats method and 
> discouraging the use of the party discipline? That could be just a 
> recommendation, or maybe a rule that would ban disciplinary actions 
> towards representatives that have voted against the party majority 
> opinion. One approach would be to introduce more structure in the party 
> structure. I have few times promoted the idea of allowing a tree like 
> structure within the parties (and between them too). That would make it 
> easier to the right or green wing of a party to vote differently than 
> the rest of the party (they could feel close to being required to do so 
> in some "right" or "green" situations).

I am thinking stock market like systems (proxy, liquid, etc..) might 
suffer from this problem as well, Larger Proxy holders would gain 
exponentially more power at they approached 50% of the voting stock.

> Also methods that do not rely on the party structure (e.g. STV) are more 
> likely to lead to a having representatives that will make independent 
> decisions, maybe sometimes working together with other right wing 
> representatives, sometimes together with other greenish representatives 
> etc.

these structures (Ireland) tend to produces very strong minority 
governments. (If I remember correctly)

> I'm not aware of methods that would take some of the power measurement 
> formula into account.
> 
> I welcome multi-winner discussions. No need and no reason to limit the 
> discussions to the single-winner theme. (What would be the reason to do 
> so? Often single-winner and multi-winner systems are alternatives to 
> each others => both needed to cover the field properly.)


cool