For some clarification, what assets are you allocating and what is the objective? Does it include stocks, bonds, real estate, etc.? Do you care about returns, volatility, drawdown, etc?
Assuming the answers are yes and you are concerned with what is usually referred to as asset allocation, I would next ask why you want to completely ignore historical price data and presumably fundamental data which provide (relative) valuation metrics?
Drawing an analogy, would you feel comfortable gambling in a casino with absolutely no understanding of the odds and payoffs involved.
However, I think you really may be asking how to do asset allocation with no assumption about return distributions or estimation of the usual statistics. This is actually not a bad question.
It seems you are ruling out risk parity which at least avoids the problematic estimation of expected returns. It is basically mean-variance optimization assuming equal Sharpe ratios and potentially using leverage. Of course, expected volatility and correlation are inputs.
Without much else to go on, I would at a minimum consider the observed long-term risk premia of assets. I would forget about bonds even without considering the dismal prospects with the current US 10-year yield below 1%.
Then I would listen to Warren Buffet and invest 90% in S&P 500 and 10% in T-bills and rebalance annually or when the equity allocation fell to 80%. As a possibly better alternative I would invest almost all my capital in the S&P 500 and spend a small amount on an equity tail-risk hedge.
Maximizing compound annual growth rate and, hence, terminal wealth is what matters to most investors. Avoiding over-diversification, mitigating drawdown, and systematically rebalancing in a smart way have, historically, made big contributions to that objective.