My understanding of the arrangement is thus:
A council tax bill is reduced by 25% from the standard (defined by your tax band) for single occupancy. If more then one eligble person is resident then the full rate is paid - if more then two people are resident then the full rate is styill payable but no premium for more than two people and is a personal arrangement as to how the bill is paid (split each way or only among those who are eligble to pay)
From memory, if one eligible person shares with other ineligble people then they lose their 25% discount.