Jorken method

Jorken method

Current convocation of the National Senate of Zhousheng has been elected using the Jorken Method

The Jorken method is a method for allocating seats in parliaments among member states, or in party-list systems. It is devised in a way, that seats assigned reach a dedicated asymptote, requiring an existence of coalition government in order to gain a majority in a house elected in that way.

Devised by a Renish mathematician Ƈestꭈ Jorken, it is currently used to allocate seats in the National Senate of the Congress of Zhousheng.

Motives

See also: Congress of Zhousheng, National Senate of Zhousheng, Zhousheng, and 2001 Zhoushi protests

Logo of the National Senate of the Congress of Zhousheng

The Jorken method, originally devised as a test concept of using a mixed electoral system, was first put into test after the 2001 Zhoushi protests led to the 2002 snap election. The method was chosen to replace the former instant-runoff method used in the National Senate of Zhousheng, and merging the 99 single-mandate constituencies into a single 99 mandate large constituency.

Equation

• s_Σ - total number of mandates available - currently set to 99
• s_Ψ - maximal number of mandates one party/alliance can recieve - currently set to 49
• s_i - number of mandates a party i recieves - can span any intiger between 0 and 49
• Π_i - fraction of votes a party i recieved (on the scale from 0 and 1) - can span any number on the interval ⟨0;1⟩
• a - variable a for setting a function

The seats are assigned using the function:

Where a is a variable that is defined in a way, that it belongs to the interval (0;∞), which is defined in a way, that the following equation holds true:

Example of usage

There are 6 parties running. They recieve the following number of votes:

Party		% of votes	Πi
	PARTY A	17.55%	0.1755
	PARTY B	3.22%	0.0322
	PARTY C	47.80%	0.4780
	PARTY D	19.12%	0.1912
	PARTY E	9.55%	0.0955
	PARTY F	2.11%	0.0211
Invalid		0.65%	0.0065

The electoral threshold is currently set to 3.5%. That means, that PARTY B and PARTY F are automatically disqualified from membership in the house. Following this disqualification, the function a is calculated, so the sum of all seats is equal to s_Σ (set to 99) using the party ceiling s_Ψ (set to 49). In this case, the constant a = 0.47. The final set of seats is therefore:

Party		% of votes	Πi	si	Scheme
	PARTY A	17.55%	0.1755	23
	PARTY B	3.22%	0.0322	0
	PARTY C	47.80%	0.4780	35
	PARTY D	19.12%	0.1912	24
	PARTY E	9.55%	0.0955	17
	PARTY F	2.11%	0.0211	0
Invalid		0.65%	0.0065	—

This result shows, the while the strongest and most popular party recieved the most seats, it is not proportionally as much as one could expect in completely proportional systems i.e. - the system makes sure, that the weaker parties are favoured in the upper house, in contrast to the lower house, where the representation is strictly proportional.

Party		% of votes	D'Hondt		Jorken	Difference
			No threshhold	3.5% electoral threshhold
	PARTY A	17.55%	17	18	23	5
	PARTY B	3.22%	3	0	0	0
	PARTY C	47.80%	49	51	35	16
	PARTY D	19.12%	19	20	24	4
	PARTY E	9.55%	9	10	17	7
	PARTY F	2.11%	2	0	0	0