IRV is better than our current system, but not by that much. Range (aka Score) Voting -- where you give each candidate a score from 1-10, like a judge in the olympics -- is much better. http://rangevoting.org/ (alias: http://scorevoting.net/) has a wealth of information on this topic, albeit in a website straight outta 2005.
It gave us prop 8, written deliberately confusing to sway the vote. It gave us prop 47, which was a truckload of measures, many good, some horrible. Resulting in a huge increase in property crimes, which was a side effect that you'd only realize if you actually read the damn thing instead of the summary. Voters don't have that attention span. It gave us prop 69, essentially a state-run DNA database - into which you're entered on arrest instead of conviction. Because "but the children" always sells.
"The notion that many people who voted "Leave" in the EU referendum now regret their vote because they didn't think "Leave" would win or they didn't realise the consequences of leaving the Single Market would be so bad." [1]
I think many of the problems of representative democracy stem from the fact that people don't read the bills, and they dont check their representatives voting history. Direct democracy seems much worse in that regard.
1. http://www.businessinsider.com/brexit-vote-regret-leave-marg...
Edit: added additional thought
Perhaps I am cynical, but I do not believe that a system which benefits the average person, the vast majority, can be accomplished in a system where the profit motive exists which is in most cases a direct contravention to the long-term wills of humanity, that is, our safe continued existence, and maintaining a relatively free way of life.
Edit: also worth looking at what has happened with previous campaigns to make the voting system fairer; in the the UK, the alternative vote referendum was opposed by those parties which drew large gains from FPTP, namely the Conservative Party. Their website compared the AV to a system in which your child wins an egg and spoon race, but he isn't given the trophy.
Political impediment: Dismantles the two party system and its vested interests.
Technology improvement: Algorithmic redistricting
Political impediment: Eliminates a strategic job security system for already-elected politicians.
Technology improvement: Cryptography
Political impediment: Eliminates a surveillance and control mechanism of politicians.
This is why we need some form of limited direct democracy. Politicians will never vote for something that directly or indirectly contradicts their own personal self interest. They won't vote for shorter term limits, bans on insider trading, stronger 4th amendment protections, ranked choice voting, objectively neutral redistricting, etc. Technology can only help us to the extent that policy and politics allow it.