Talk:Hare quota

counting algorithm wrong

the counting algorithm is wrong. the quota needs to be subtracted at each step, even if there aren't enough first choice votes. otherwise the voters are over-represented.

the remainder should

--- votes:

ab-12 ba-7 rs-9 sr-8

--- step 1:

plurality is a 12 first choice votes subtracted, 0 remaining to subtract no surplus votes

remainder: b-7 rs-9 sr-8

--- step 2:

plurality is r 9 first choice votes subtracted, 3 remaining to subtract proportionally 3 second choice votes subtracted proportionally no surplus votes

remainder: b-7 s-5

-- step 3:

plurality is b 7 votes subtracted no surplus votes

remainder: s-5

--- result:arb

---

otherwise in step 2 you're only subtracting 9 votes. so those voters would get over-represented 12/9 = 133%. they'd essentially be getting 1.333... votes instead of 1, violating the 1 person 1 vote rule.

Kevin Baas^talk 17:33, 29 March 2016 (UTC)

technically inferior

I corrected what i thought as undue criticism of Hare quota, and disregarding its use outside STV. Quite a few sources claim it, along Sainte-Lague, gives most proportional results (though Im personally sceptical that Sainte-Lague could give equally perfect proportionality to Hare quota), and thats hardly an unimportant advantage in comparison to Droop. It also seems to me to be equivalent to the most obvious definition of proportionality, i.e. that percentage of seats a party gets is equal, within the rounding margin of error, to the percentage of votes (since (Vp/Vt)*S=Vp/(Vt/S) Vp being votes a party won, Vt the total num of votes, and S the num of available seats). Seeing how precise STV methods get sofisticated and computationally intensive anyways, finding a quota that allocates as much places as possible prior to fractions and transfers doesnt seem like an important saving. Btw does anyone know more about QPQ method and its Swedish predecessor, and its (incredibly small?) computational intensity, and has any data on its proportionality?--Aryah 03:03, 19 July 2006 (UTC)

majority rule

I dont understand why such a fuss is made out of the fact that Hare quota can give a minority of seats to a majority of votes (btw it has a significantly smaller problem with this than Sainte-Lague) - giving more than 1/2 of the seats to a party of more than 1/2 of the votes is not mathematically more important (thus making it not a technical but a political flaw) than giving more than 1/3 of seats to a party of more than 1/3 of votes, or more than 1% of the seats to a party of more than 1% of the votes, and all of this cannot be simultaneously satisfied with the system of allocating the seats. It is not related to proportionality, but is a political demand - so it seems quite appropriate for it to be satisfied at the end of the calculation, by giving some premium seats to the majority party - an ad-hoc sollution to an ad-hoc problem. It certanly doesnt seem to be a sufficient reason to sacrifice superior proportionality throuought the calculation, that Hare ensures. Particulary not on such a way, as with Hagenbach-Bischoff quota needed for this majority rule ensurance, as to open the possibility of aditional bias of giving more seats to some constituancies than to others --Aryah 05:50, 19 July 2006 (UTC)

The numbers in the example are too nice

Hello,

in the example there are 100 votes and 2 seats. The latter divides the first, making the example unrealistically simplistic. It would be more interesting to see how they deal with non integer fractions (it can be of importance!) Evilbu 13:04, 22 October 2006 (UTC)

Can this or the Huntington-Hill method, sometimes called "method of equal proportions" be clarified or justified?

After this recent Judd Gregg and US Census flap, I've been considering the hot potato that apportionment of US Representatives will be after 2010. One problem is that of counting (who to count and who not to), but that's a different problem than what is concerning me at the moment. So, assuming we have undisputed census figures for each state, the (hopefully blind and objective) mathematical method for determining how many Representatives each state gets sure seems different than what is depicted at United_States_Congressional_Apportionment#The_Equal_Proportions_Method.

The constraints applied to this problem is that the total number of Representatives is fixed and determined in advance by law; 435, and that each state, even the least populous, must get at least one Representative.

Let

$K\$ be the number of states (currently 50).

$1\leq k\leq K\$ be the index of k^th state. It doesn't matter how they're ordered.

$P_{k}\$ be the agreed census population for the k^th state.

$P=\sum _{k=1}^{K}P_{k}\$ is the total population of all K states (excluding DC and the territories).

$N_{k}\$ is the number of Representatives for the k^th state that we are trying to determine.

$N=\sum _{k=1}^{K}N_{k}\$ is the total number of Representatives in the House for all K states (excluding DC and the territories) which is currently 435.

$q>0\$ is the nationwide constant of proportionality or quota ratio for proportionately allocating Representatives or a state as a function of its population.

So, if we could actually have fractional numbers of persons as Representatives,

$N_{k}\ =\ q\ P_{k}\quad \quad \forall \ 1\leq k\leq K$

$\sum _{k=1}^{K}N_{k}\ =\sum _{k=1}^{K}\ q\ P_{k}=q\sum _{k=1}^{K}P_{k}$

or

$\ N=qP\quad$

$\ q={\frac {P}{N}}\quad$

But, of course, we cannot divide Congressional Representatives into fractions even if we might like to tear them apart on occasion. Each states House delegation must be an integer number of people at least as big as one. Wouldn't this mean:

$N_{k}\ =\lceil q\ P_{k}\rceil \quad \quad \forall \ 1\leq k\leq K$ ?

where

$\lceil x\rceil =\min \,\{n\in \mathbb {Z} \mid n\geq x\}$ is the ceiling function (which means always round up).

Now if q>0 was arbitrarily small (but positive), then each state would get 1 Representative. It wouldn't be particularly well apportioned and it wouldn't add up to N=435. We want

$N=\sum _{k=1}^{K}N_{k}=\sum _{k=1}^{K}\lceil q\ P_{k}\rceil \$

Then couldn't q be increased monotonically, thus increasing some of the N_k and $\sum _{k=1}^{K}N_{k}=\sum _{k=1}^{K}\lceil q\ P_{k}\rceil \$ until it reaches the legislated N=435 value? Would that not be the meaning of proportional representation with the constraints that N_k must be an integer at least as large as 1? How is there any paradox in this method (assuming that, as q increases we don't have two states simultaneously increasing their integer N_k and the total jumping from 434 to 436) and where the heck does that Huntington-Hill method that is depicted at United_States_Congressional_Apportionment#The_Equal_Proportions_Method come from? How does that possibly have anything to do with true proportional allocation of a fixed number of seats in the House?

Can someone explain this? 96.237.148.44 (talk) 01:57, 14 February 2009 (UTC)

Answered at Talk: Huntington–Hill method #Can the Huntington-Hill method, sometimes called "method of equal proportions" be clarified or justified?. --84.151.17.20 (talk) 23:11, 17 November 2009 (UTC)