I am trying to understand the difference between allocation and score spending. The relevant system for allocation is just the standard allocation after the KP_Transform. For spending score the system is Sequentially Spent Score ( SSS )

Lets run some scenarios and ignore surplus handling so we can look at 1 ballot. A useful ballot for a max score 5 system is.

A:1 B:3 C:4 D:0

The KP-Transform turns this into 5 approval ballots.

A B C D

1 1 1 1 0

2 0 1 1 0

3 0 1 1 0

4 0 0 1 0

5 0 0 0 0

**If D is elected**

Both ballots stay the same in Allocated KP and SSS

**If C is elected**

In SSS 4 is subtracted from the points to spend and it goes to A:1 B:1 C:N/A D:0

In Allocated KP ballots 1-4 are exhausted and the 5th does nothing so the voter is done

**If B is elected**

In SSS 3 is subtracted from the 5 points to spend and it goes to A:1 B:N/A C:2 D:0

In Allocated KP ballots 1-3 are exhausted leaving

A B C D

1 0 0 0 0

2 0 0 0 0

3 0 0 0 0

4 0 0 1 0

5 0 0 0 0

which is equivalent to A:0 B:N/A C:1 D:0 different from SSS

**If A is elected**

In SSS 1 is subtracted from the 5 points to spend and it goes to A:N/A B:3 C:4 D:0

in Allocated KP ballot 1 is exhausted leaving

A B C D

1 0 0 0 0

2 0 1 1 0

3 0 1 1 0

4 0 0 1 0

5 0 0 0 0

which is equivalent to A:N/A B:2 C:3 D:0 different from SSS

There is clearly a difference between spending and allocation.

The best way to summarize the difference is that Allocated KP takes a ballot, **B**, and subtracts the score to the winner, **S**. Giving a simple **B-S**. While SSS takes into account the max score, **M**, and follows the formula **min(M-S,B)**.

The question is which is better. SSS was designed to follow the concept of Vote Unitarity which as its inventor I clearly favour. What are other people opinions?

If the formulas above are accurate we could just have a new system for Allocated KP but use the **B-S** method on the original score level with no need for the KP transform. This is likely simpler to explain to the public.

Is there a real difference in surplus handling? The example above ignored that so that I could explain better. I think the ballots are scaled differently there too since in SSS the whole ballot is handled as 1 but in Allocated KP each score point is handled independently.