In this strangest of all Senate elections, he is probably the only senator elected because people mistook his party for another. In NSW seats in the House of Representatives, the Liberals and Nationals won 47.3 per cent of the vote. Yet in the Senate, they won just 34.2 per cent. It's a reasonable inference that almost one in five people who voted for the Liberals or Nationals in the lower house mistakenly put a 1 in the box of the Liberal Democrats when it was the first thing they saw on that congested Senate ballot paper. By contrast, in Victoria, where the Liberal Democrats faxed their Senate voting ticket to the wrong number and were listed only below the line, they won just 363 votes. The Coalition polled much the same in both houses: 42.7 per cent in the House, 40.1 per cent in the Senate. The comparison suggests the confusion of names between Liberals and Liberal Democrats cost the Liberals half a million votes in other states - and a Senate seat in Tasmania. But there were many other weird results and near misses. Eight of the 76 senators will be on the crossbenches, representing five different parties. And for the first time since the demise of the original DLP 40 years ago, the Coalition will now face competition from within Parliament for votes on the right. Leyonhjelm is the best example. A libertarian purist, he wants government wound back to a minimal role in society. His causes include repealing gun laws, raising speed limits, selling settlers' visas to asylum seekers for $50,000, and decriminalising drugs, incest and voluntary euthanasia. The LDP platform aims to ''limit the federal government to defence, immigration, basic public services (e.g. passport services, regulation of hazardous materials, air and sea transport regulation), and assistance to the least well-off''.

It's a utopian platform, but it will appeal to many on the right - and as we saw when he appeared on 7.30 recently, Leyonhjelm is a smart cookie who argues his case well. Expect to hear a lot more of him - and of Clive Palmer, and Nick Xenophon, and Family First's Bob Day, an Adelaide builder who worked alongside Abbott in the '90s as a fellow monarchist and who will aim to hold the Liberals to a conservative agenda on both economic and social fronts. While the new Senate parties could end up as just a temporary irritant to the Liberals, there is potential for them to develop into something more - as the Greens have become more than a temporary irritant to Labor. Even the temporary irritants could be substantial, especially if the Palmer United Party ends up winning one of the final seats in Western Australia (which might not be known for some time, as whoever loses will appeal to the High Court, which could well order a recount). The Abbott government should have a majority to abolish the carbon tax and mining tax once the new Senate takes its place next July. But it will have to negotiate its paid parental leave plan with the Greens, and will struggle to win Senate backing for tougher laws against asylum seekers, or its friendless ''Direct Action'' plan to pay polluters to reduce their emissions. Then there are the future issues we don't know about yet. They will be a continual challenge, especially if the government needs the support of the unpredictable Palmer for any legislation opposed by Labor and the Greens.

One suspects that one of the first items to be dealt with while the old Senate lasts will see the Abbott government sitting down with the Albanese/Shorten opposition to negotiate Senate electoral reform - party registration, party names, electoral deposits, and changing the voting system - to ensure that we never have an election like this again. In some ways, this was less an election than a lottery. Apart from Leyonhjelm winning a seat because voters thought he was a Liberal, it has seen: ■A new senator elected with a record low of just 0.5 per cent of the votes, to represent a party with no policies, and then going to ground to avoid media questioning. (Ricky Muir, of the Australian Motoring Enthusiast Party, elected in Victoria on preferences from 23 other parties, whose voters intended their vote to be for someone else). ■A colourful sex industry lobbyist with fewer than 5000 first preferences get to within 245 votes of winning a seat in a state he has never lived in. (Robbie Swan of the Sex Party, almost elected in Tasmania). ■A key figure in the new government come within 0.05 per cent of losing his seat a week after being sworn in to the ministry. (Arthur Sinodinos of the Liberals, almost unelected in NSW).

■A senator from a party that wants to ban coal mining elected on the preferences of a party run by an aspiring coal baron (refugee advocate Sarah Hanson-Young of the Greens, re-elected in SA with the help of refugee supporter Clive Palmer), and vice versa (Jacqui Lambie of the Palmer party, elected in Tasmania with the help of the Greens). ■Two seats in one state decided jointly by just 14 votes that separated two parties with almost identical votes when one or other had to be eliminated. (Western Australia, where the Shooters' party outpolled the Australian Christians by 0.001 per cent of the vote, thereby possibly securing the final two seats for Labor and the Palmer party instead of the Greens and the Australian Sports Party). ■One party win first or second place on crowded ballot papers in four of the six states, which resulted in it winning one seat and coming close in two others (the Liberal Democrats, who drew first place in NSW, second in Victoria, WA and Tasmania, and fifth in SA). Winning a seat in the Senate in 2013 was like winning a lottery. Voters did not where their votes would end up, or who they would be electing. We thought it bizarre when Family First's Steve Fielding was elected from Victoria in 2004 with just 1.9 per cent of the vote. But that was a landslide compared with Ricky Muir's 0.5 per cent, let alone the 0.2 per cent that could give Wayne Dropulich of the Sports Party a seat in WA if a recount overturns the result.

In every state except Queensland, a tiny shift in votes would have seen a different result: 0.001 per cent in WA, 0.04 per cent in Tasmania (electing the Sex Party instead of Lambie), 0.05 per cent in NSW (electing the Shooters party instead of Sinodinos), 0.05 per cent in Victoria (electing the Liberals' Helen Kroger instead of Muir), and 0.15 per cent in SA (electing the No Carbon Tax Climate Sceptics party instead of Day). Is this the Senate system we want? There are many options for reform, some already working at state level. Senators should be elected because people vote for them, not because they negotiate good preference deals. The $2000 deposit required of Senate candidates is too low to deter preference-seekers, while a party can be registered with just 500 members, so the LDP has three satellite parties also farming votes for it under different names. Most proportional representation systems overseas set a threshold to ensure that parties win seats only if they have significant support: in New Zealand and Germany, parties must win 5 per cent of first preferences to win seats. Most states have swept away the archaic rule that people voting below the line must number every square. NSW has banned party tickets. A 1 in the box above the line is a vote only for that party's candidates. You may give preferences, but only if you choose to fill in other boxes above the line. If the goal is to put power in the hands of the voters, then Tasmania and the ACT are the state of the art. Positions on the ballot paper are rotated around, so there are no donkey votes, no party tickets, and party candidates compete (amicably) with each other for votes, as well as (less amicably) with their opponents. In the ACT, only one preference is required, in Tasmania five, but voters can write in as many as they like.

But that leaves the Liberals still at risk from voters confusing them with the Liberal Democrats. The blame ultimately rests with the Chief Justice of the High Court, Robert French, and two other judges, who in a 2001 case directed the Australian Electoral Commission to register the Liberals for Forests group. Their judgment in the Administrative Appeals Tribunal set the precedent that in 2008 made the commission, despite strong misgivings, finally give way and register the LDP as the Liberal Democrats. ''It is unlikely that any elector, seeing the two names on a ballot paper, will draw the conclusion that 'Liberals for Forests' is a political party related to the Liberal Party of Australia'', the judges wrote. ''The possibility that the name 'Liberals for Forests' could be mistaken for … 'Liberal' is, in the opinion of the Tribunal, not such … that there is a real chance that it will occur.'' On Saturday, September 7, almost 10 per cent of NSW voters voted for the Liberal Democrats. The evidence suggests the vast majority of them did so because they thought they were voting for the Liberal Party. The Abbott government, with Labor, now must work out how to act retrospectively to protect each other's brand names in future.