The veil of ignorance is a concept first introduced by John Rawls in "Towards a Theory of Justice". It is an imaginary veil behind which you know nothing of your race, sex, abilities, etc. and you become an unbiased, moral person able to exert free will. From behind "the veil" you can make decisions that aren't designed to benefit yourself but are based on "higher" criteria of justice and fairness.
But the real world doesn't work like this. We all have our biases, some of which we may not even be aware of. As this attorney writes, pressure groups manipulate democracy to formulate laws to benefit themselves. They may be well funded and powerful. Perhaps the only way of undermining their power is to implement more direct democracy. Interactive Democracy gives us all a chance to come up with a majority view less distorted by money and political connections. It doesn't use a fictional "veil of ignorance" to achieve justice, but balances one bias against another to get a similar effect.