To ensure a fair distribution of votes, a mixed compensatory PR system involves detailed workings. It is best illustrated by way of a hypothetical example.

Imagine that a given state has 32 constituencies. Suppose that parties W, X, Y and Z contest each constituency. A total of 32 seats are to be allocated for the State. Suppose also that on election day, 100,000 electors vote. How would a mixed compensatory PR system operate in this scenario?

Under a mixed compensatory PR system, each voter has two votes. One vote, called the Constituency-Based vote, relates to electing an individual as member in the Lok Sabha to represent the local constituency. These votes are tallied on a constituency-by-constituency basis, employing a FPTP system. The second vote, called the Party-List vote, is for a party.

These votes are tallied on a state-wide basis, following a PR system.

In the Lok Sabha, approximately half of the seats representing a State are Constituency-based seats, and the other half are Party-List seats. Therefore, in our example 16 seats will be allocated from the Constituency-based votes, and 16 seats will be allocated from the Party-List votes.

Suppose that in our hypothetical example, the share of the Party-List votes is as follows:

Party	Actual Number of Votes Received	Percentage of Party-Vote Won
W	37000	37
X	35000	35
Y	9000	9
Z	19000	19
Total	100000	100

Our Mixed Compensatory PR model compensates a 10% threshold for Party-List votes. This means that for a party to be allocated any Party-List seats, it must frist receive atleast 10% of the Party-List votes. Click here for explanation of rationale of threshold

In the hypothetical example, Party Y has only received 9% of the Party-List vote thus failing the threshold. Party Y is ineligible for Party-List seats. For the purposes of distributing Party-List seats, Party-List votes for Party Y are disregarded.

Thus the total valid Party-List votes would now be 91000.

Under a mixed compensatory PR system, the aim is to ensure, to the greatest extent possible, that the total number of seats won by each party reflects the proportion of the vote received by the party. To do this, we calculate the number of total seats to be allocated to each party, based on each party's share of the valid Party-List votes. Keeping in mind that invalid votes, such as those Party-List votes for Party Y in our example, are disregarded.

The totals are calculated using the following formula:

Number of Valid Party-List votes obtained by the part

Total number of seats

Total number of valid Party-List votes

Using this formula, the allocation of totals in the hypothetical examples are as follows:

Party	Actual number of Party-List votes received	Number of Party-List votes won	Number of valid Party-List votes won	Nominal maximum number of total seats to be won
W	37000	37	40.66	37000/91000*32=13.01=13
X	35000	35	38.46	12.31=12
Y	9000	9	0	0
Z	19000	19	20.88	6.68=7
Total	100000	100	100	32

It must be understood that this number is the entitlement of the party, while the manner of filling the seats is subject to adjustment based on results in FPTP elections (See steps below)

It should also be noted that in this illustration, seats are allocated using the 'highest remainder method.' Obviously, seats can only be distributed as whole numbers. Thus, if any party is entitled to a remainder of a seat, the party with the highest remainder will receive the remaining seat. In our example, Party Z is notionally entitled to 6.681 seats. This automatically entitles it to six seats, and because it has a highest remainder out of the parties, it is also entitled to a seventh seat.

Constituency-based seats, as discussed previously, are determined via FPTP system. Suppose that in our hypothetical example, the constituency-based seats were actually won as follows:

Party	Constituency-based seats won
W	9
X	4
Y	2
Z	1
Total	16

We determine the number of party list votes to be allocated to each party by using the following formula:

Number of Party-List seats to be allocated to each party

=

Total number of combined seats to be allocated to each party

-

Actual number of constituency-based seats won by each party

Using this formula, the number of Party-List seats to be allocated to each party in the hypothetical example is as follows:

Party	Total number of seats that can be won	Actual number of constituency-based seats won	Number of Party-List seats allocated
W	13	9	4
X	12	4	8
Y	0	2	0
Z	7	1	6
Total	32	16	18

The previous table shows an effect that may seem incongruous at first: the total number of seats actually won (16+18=34) is greater than the nominal total number of seats to be allocated (32). The reason for this is under a Mixed Compensatory PR system, parties who fail the threshold are entitled to retain consituency-based seats. These retained seats create a surplus of seats. These surplus seats are called 'overhang' seats.* To accommodate this surplus, the total number of seats is expanded to include overhang seats. Sometimes, these surplus seat could also be because non-party, 'independent' candidates won FPTP seats.

In our example, Party Y failed the 10% threshold, and thus was ineligible to receive any of the Party-List seats. However Party Y won 2 constituency-based seats, which it is entitled to retain. These 2 seats become overhang seats and the total number of seats for the state increases correspondingly to 34.

After adjusting for thresholds and overhang seats, the final results are as follows:

Party	Percentage of Party-List votes received	Percentage of valid Party-List votes received	Nominal maximum number of seats that can be won	Number of constituency-based seats won	Number of Party-List seats allocated	Final actual total seats won	Percentage of total seats (for all parties won)
W	37	40.66	13	9	4	13	13/34=.3823
X	35	38.46	12	4	8	12	.3529
Y	9	0	0	2**	0	2	.0588
Z	19	20.88	7	1	6	7	.20588
Total	100	100	32	16	18	34	100

*It should be noted that parties that reach the threshold also receive overhang seats. For example, if a party's notional maximum number of total seats was 2 (based on its share of the valid Party-List vote), but it won 5 constituency-based seats, it would have a total of 3 overhang seats. A overhang seat is thus best defined as a party's consituency-based seat won in excess of a party notional maximum number of total seats.

** These seats are the overhang seats, which Party Y is able to retain despite not reaching the 10% threshold for being eligible for Party-List seats.

While the mixed compensatory PR system may seem complicated at first, it actually is relatively easy to implement in practice. More importantly it leads to much fairer allocation of seats than the current FPTP system. Let us compare the operation of the mixed compensatory PR system versus the current FPTP system in the hypothetical example:

Party	Percentage of Party-List vote obtained by parties	Total seats won under a compensatory mixed PR system	Total seats won under a pure FPTP system*	% of total seats (for all parties) won under mixed compensatory PR system	% of total seats (for all parties) won under a pure FPTP system
w	37	13	18	13/34=38.23	18/32=56.25
x	35	12	8	35.29	25.00
y	9	2	4	5.88	12.50
z	19	7	2	20.59	6.25
Total	100	34	32	100.00	100.00

* This is based on the assumption that if all seats are elected under the FPTP system, the seats won by parties would be double the number of constituency-based seats won by them (in the mixed system).

The benefits of a PR system, as compared to a pure FPTP system, are obvious:

• Under the FPTP system, Party W enjoys a disproportionate share of seats, despite only having slightly more support than Party X throughout the State. Under the PR system, each party's share of votes better reflects their relative shares of State-wide votes.
• Party Y, which has highly-localized interests and does not receive much State-wide support, receives fewer seats under the PR system. This encourages parties to adopt broader-based policies.
• Party Z is under-represented in the allocation of seats under a pure FPTP system. Under a PR system, it receives an adequate number of seats to reflect its substantial minority support from the State-wide electorate.