Well theres also reason to question the size of x. If substantial amounts of money are wasted in the effort of allocating x, might it be better to just use that

Well theres also reason to question the size of x. If substantial amounts of money are wasted in the effort of allocating x, might it be better to just use that money to increase x and go for a simpler allocation model. For example equal amounts to everyone. After that you must consider the systematic effects. If you do manage to increase x and allocate it to the poor. What will it do to the economy? There is a chance that it will feedback into increased tax revenue, which again raises x. More money allocated to the poor means more money spent on things needed by the poor, which means increased demand for certain goods and so forth. It's also possible that the same poor, now equipped with secure funding, starts new business to fill that demand which creates jobs and more taxable incomes.