This idea is similar to "Increased Entropy Government", but there are some fundamental differences in motivation and execution, so bear with me.
One problem with our current system of democracy is that only two types of people tend make it to the top:
a) Ultra ambitious, power-hungry sociopaths.
The way to the top is long and cut-throat competition weeds out the more mellow types. These personalities are quite often very talented, but once in power, they tend to use their talent in their own selfish interest rather than the interest of the voters.
b) Priviledged upper class types. Their loyalty to the super-rich and mega-corporations means that they have the funds for election campaigns, but once they are in power, whos interests do they represent? Certainly not the interests of the people who voted them.
The alternative: choosing a president randomly.
It works like this: Any citizen over 35 without a criminal record can take part in this lottery. He/she also needs to take a series of tests to ensure a minimum IQ and absence of mental illness. Every two years a president is chosen at random from the ballot.
The role of the president is decide on the general long term direction of the country, much like the current president. Specific, day-to-day running of the country would still be done by a democratically elected congress. After two years the president would return to the normal life s/he was leading before.
The average Joe from next door has a better understanding of the
average people's needs than an out-of-touch career politician.
They will certainly not make the perfect leader, but one thing is certain: They are unlikely to be the dishonest and manipulative crook that the average politician is.