[chezlaw]

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Stick some arbitary numbers on it.
Ihe payrise makes me 100 units more happy
The unhappyness of my co-workers makes me 50 units less happy.
Each of my 100 co-workers is 1 unit less happy if I take the rise.

maximising my own happiness:
payrise = +50 units

maximising everyones happiness
payrise = +50 units - 100 * 1 units = -50 units

So maximising my happiness conflicts with maximising everyones happiness. The two things are different and I can't see how you can make them the same.

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The second equation is ALSO your own happiness. Duh. Re-read what you wrote.

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The second equation is
increase in my happiness = +50 units
decrease in others happiness = -100 units

Net change in happiness over everybody = -50 units

???

chez