Direct income inequalities from trade are inevitable in any market. Incomes cannot be distributed evenly in the first instance because people do not spend evenly. When people trade it is always the case that some products and ideas are more popular than others, and as soon as money becomes economically necessary some people accumulate more wealth than they can consume immediately, and imbalances occur.
Free and open trade with a common currency (or easily convertible currencies) is the only efficient mechanism for determining what is needed and distributing limited resources in complex societies. Central control cannot supplant free trade, as production and distribution decisions are too complex for this. Attempting to do so limits diversity, freedom and growth.
Because direct income equality from free trade is impossible, and free trade is vital, a shared base income, ensuring equal opportunity for all to realise potential, must be created by sharing the earnings made on trade.
Shared earnings and a shared base income do not eliminate income inequality, some will still earn incomes far greater than the average, but sharing half of all income earned from trade, via a base income shared between all, helps eliminate poverty and ensures all people have the opportunity to realise their potential. It also inculcates a common spirit of sharing in society, a sense of community and belonging.
Why half? Because it is an equal share, half for ourselves, half for others. Such a share is also simple - simple to comprehend and simpler to implement than any tiered system.
How a shared income is structured accords to the society in question and what works, through a range of direct (monetary) and indirect forms (universal healthcare, free education). The key is that the steps taken are considered and constructed to further fulfilment without harm.
[Excerpt from The Common Purpose Manifesto]