There's a delay regardless of whether or not two different blocks are solved at the same time?
Yes but if a miner knew that no other block would be found in the next x seconds they wouldn't care. Since that can never be known the longer the propagation delay the higher the probability that a competing block will be found before propagating completes and potentially win the race.
You mean that when two different blocks are solved at the same time, the smaller block will propagate faster and therefore more miners will start building on it versus the larger block?
Yes although it is more like the smaller block has a higher probability of winning the race. A miner can never know if he will be in a race condition or which races he will lose but over the long run everything else being equal a miner with a longer propogating delay will suffer a higher rate of orphaned blocks.
Is there a straightforward way to estimate the risk of an orphan?
Not that I know of. I do know pools have looked into this and to improve their orphan rates to remain competitive. My guess is any analysis is crude because it would be difficult to model so testing needs to be done with real blocks = real earnings. A pool at least wants to ensure its orphan rate isn't significantly higher than its peers (or global average).
Even with a separate overlay, two blocks solved at the same time is a problem. And I would imagine that adding a new overlay is an extreme solution to be considered as a last resort only.
True but if it became a large enough problem, a mining network would allow for direct transmission to other miners. A block notification superhighway of sorts. Blocks could be digitally signed by a miner and if that miner is trusted by other miners (based on prior submitted work) those miners could start mining the next block immediately. This of it as WOT for miners but instead of rating financial transactions miners are trusting other miners based on prior "good work".
The propogation delay on large blocks is a combination of the relay -> verify -> relay nature of the bitcoin network, combined with relatively slow block verification (large fraction of a second), and the potential need for multiple hops. All combined this can result in a delay of multiple seconds before a majority of miners start work on this block.
A single hop, trust enough to start work on next block, and verify after the fact would make the "cost" of a larger block negligible. It is just an idea. I care less about mining these days so that is something for major miners to work out. Even if this network never became "official" I would imagine some sort of private high speed data network to emerge. It would allow participating miners to gain a small but real competitive advantage on other miners. Less orphans, ability to include more tx (and thus higher fees) = more net revenue for miners.
What are your thoughts on the last scheme I described?
Any system which relies on trivial input can be gamed. I (and other merchants) could buy/rent enough hashing power to solve 1% of blocks and fill them with tx containing massive fees (which come right back to us) and inflate the average fee per block.
I would point out that a fixed money supply and static inflation curve is non-optimal. In
theory a central bank should be able to do a better job. By matching the growth of the money supply to economic growth (or contraction) prices never need to rise or fall (in aggregate). A can of soup which costs $0.05 in 1905 would cost $0.05 today. At least the inflation aspect. The actual price may vary for non-inflationary reasons such as improved productivity or true scarcity of resources.
The problem with central banks isn't the theory ... it is the humans. The models of monetary policy rely on flawed humans making perfect decisions and that is why they are doomed to failure. Flawed humans choosing the benefit for the many (the value of price stability) over the increased benefit for the few (direct profit from manipulation of the money supply). Maybe someday when we create a utopian such ideas will work but until then they will be manipulated for personal benefit.
The value of Bitcoin comes from the inability to manipulate the money supply. Sure many times a fixed money supply and static inflation curve is non-optimal but it can't be manipulated and thus this non-optimal system has the potential to outperform systems which in theory are superior but have the flaw of needing perfect humans to run them.
On edit:On rereading I noticed you proposed using median block reward not average. That is harder to manipulate. It probably is better than a fixed block size but I would expect 50 BTC per block isn't necessary on a very large tx volume so it may result in higher than needed fees (although still not as bad as 1MB fixed). It is worth considering. Not sure if a consensus for a hard fork can ever be reached though.
Hmm...this seems problematic. If the transaction volume doesn't grow sufficiently, this could kill fees. But if the transaction volume grows too much, fees will become exhorbitant. IF we accept that max block size needs to change, I believe it should be done in a way that decreases scarcity in response to a rise in average transaction fees.
Likewise a fixed subsidy reduction schedule is non-optimal. What if tx fees don't cover the drop in subsidy value in 2016. Network security will be reduced. Should we also make the money supply adjustable?
(Kidding but I hope it illustrates the point).
TL/DR: Fixed but non-optimal vs adjustable but manipulable? Your choice.