Curious question:

Why is the GINI coefficient so low, and income so high in the one western country that doesn't have a federal minimum wage?

I'll let you guess which country it is. The results may surprise you

At first I thought you were talking about the US but considering most European countries have a lower GINI coefficient than the US and my country doesn't have a federal minimum wage I'll go with Germany

Edit: I know we don't have the highest income But the way you said "the ONE western country" pushed me into writing this

Wait a second. If over 40% doesn't pay federal income tax, then how am I doing as a part time student worker for a public university making a bit of minimum wage.

That is one way of looking at it.  Another way would be that the groups and minorities you've listed are now worse off for the fundamental flaw in this IR legislation = a minimum wage lowers available jobs.  Unskilled people are now being pushed out of the market and are completely dependent on welfare, because businesses can't afford to hire more people for less and build up their skillsets and experience with a minimum wage in place.  Not saying that I advocate this point of view, but the argument has merit. 

I would guess Denmark because they have a population that is practically all trained for very specific skillset... as such is easy for them to lose jobs, regain jobs and the rest... and also have lots of unions that well, work good instead of like US unions.

Not sure what their gini coefficent is, but Denmark tends to serve as the model of a europeon country now a days that all the other countries try and copy but usually can't because they are too big and to diverse.

"Average" minimium wage in Denmark is like... $18 US.

Really Denmark is an intriguing combination of extreme socialism mixed with extreme capitalism, rather then the half hearted compromises that usually exist.

Doesn't ever seem to work on a larger scale though.

Hard-line piety is not the answer to helping the US economy. Just say no because it is not in the Bible/Constitution is going to do more harm than good. Job creation is the answer. Obama and his team are doing the best they can and they should be given a fair go. 

More jobs and more things made in America. Buy American products and invest in America. Say no to Made in China and buy fewer imported goods. America will never turn back its progress on civil rights just that it can be more competitive with cheap foreign labour markets that disregard human rights. America is not China. 

Neo-conservatives rarely  do not provide a good economic policy debate on why lowering the minimum wage  or abolishing child slave labour laws are good for the American workers. The political rhetoric nonsense may win a political debate if it is repeated enough over and over and brainwashes the masses. Upsetting minority groups who will be impacted by a draconian  hard-line political move would be met with mass protest and civil unrest. 

The one Western country? I don't think any of Scandinavia does. Nor does Switzerland to the best of my knowledge.

Scandinavia gets away with it through having powerful unions negotiate informal but accepted minimum wages for every sector I believe.  I suppose they've figured that there is no reason to change their current system if it isn't being abused.

Edit: Heres a map that shows that a swathe down the middle of Europe has no minimum wage.

http://epp.eurostat.ec.europa.eu/cache/ITY_OFFPUB/KS-QA-09-029/EN/KS-QA-09-029-EN.PDF

Also found it interesting in my research that NZ was the first country to have a minimum wage =P.

Well he said "federal" and there are several european countries without a federal minimum wage. Denmark doesn't have minimum wages but they have stronger wage agreements than Germany if I remember correctly. So Denmark isn't the "only" country to have it (Italy and Norway don't have minimum wages either).

Before we get into whether or not these systems and ideologies are good/bad, the point was whether or not they are unconstitutional at a Federal level. I don't know whether they are, I haven't studied much of the constitution in any great detail - but if they are, something needs to change (either removal/reform of the systems to make them comply with the constitution, or reforming the constitution so that it complies with the existence of the system). The precedent set forward by Government's ignoring the constitution and getting away with it for decades on end is a worrying one, and, frankly, removes the legitimacy of the constitution as a means for governing the country.

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Now, let's get onto the area of discussion that is (wrongly) causing the most controversy:

Working time, sick pay, vacation, and wage control legislation are all ridiculously focused on the extreme short-term, and it's obvious why: the short-term is the only term politicians can focus on, when they face the public vote every few years. Of course, it really leads you to question the motives of the politicians when they seem to favour saving their, and their party's, hides over the long-term benefit of the people that they're supposed to be working for.

Fortunately, in the UK, we have now got a Government in who's priorities are slightly more in-line than they would usually be, and are now focussing on reforming many key sectors, and tackling the deficit now - before the markets have forced them (which is something that cannot be said for most of the rest of the world). Of course, they still promised to "preserve" the NHS... which is quite possibly the largest time-bomb in the country, I just hope that they win the confidence in the people enough in this term to allow them to reform the NHS in the next.

Back on-topic, though, the main issues of worker's rights policies is that they stifle economic growth. Basically, anything done to inflate the employment market now, will cause the market to rectify itself in the long run. By saying that these two guys can get paid a minimum of £x per hour, which will most probably be above what the market deems their contribution to be worth, we increase the costs to the firm, which will have a distortion effect which ripples throughout the entire economy, reduces profitability, and, therefore, reduces further investment: by forcing a firm to pay these two guys £x this year, we could preventing a third guy from getting a job at all next year.

Essentially, by inflating things artificially today, we cause tomorrow to be slightly worse. The questions remain: would society be better or worse off today if it wasn't for systems such as Social Security, minimum wage legislation, and all sorts of other employment legislation. Well, that all depends. Employment in the southern states wouldn't be as attacked from illegal migration today as it is now, and the USA wouldn't be losing as many jobs to Asia as it currently is. On the whole, the USA is still probably better off today than it would have been without the systems, but we are the tipping point. As Asian development picks up, jobs will be lost at ever-greater paces, and the deficit holes left by SS/Medica(ir/id) will cripple the country over the coming decades.

Just look at places like Detroit, Michigan - one of the most "progressive" parts of the USA. Went from being a flag-runner of USA capitalism, to becoming one of the worst places in the USA to live, in a really short space of time. It had some of the most favourable employment rights in the country, and now its key sector (automobiles, for those who really didn't know), is now being shredded to pieces by foreign firms.

How's the Californian economy coming along?