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* Merkel's CDU overestimated their support in Lower Saxony
* Strategy of lending votes to coalition partner misfired
* Policies outweigh personality in Germans' voting choices
* Lessons for Chancellor 8 months before national vote
By Stephen Brown and Alexandra Hudson
BERLIN, Jan 21 (Reuters) - If Angela Merkel's conservatives draw any lesson from the latest election setback in Lower Saxony state for her bid for a third term as chancellor, it is this: don't bet that her popularity will automatically translate into votes.
Encouraged by half-Scottish state premier David McAllister's confident campaign, Merkel's Christian Democrats (CDU) thought they could afford to give supporters tacit approval to split their ballots to save their struggling Free Democrat (FDP) allies.
The strategy backfired. Badly.
The FDP, which has a record of confounding forecasts of its demise, far surpassed the 5 percent threshold for entering the state assembly with a surprising 9.9 percent of the vote.
"A substantial number of voters deliberately voted for the FDP in order to be absolutely certain that we would get into the assembly, and that I would stay in power as state premier," said an ashen McAllister on Monday.
The CDU could ill afford to lose those votes. It remained the biggest party at 36 percent but lost more than 6 percentage points from the last state vote, resulting in a loss of power to the Social Democrats and Greens, who clinched a majority of just one seat, which Merkel said made defeat all the more painful.
The result put wind in the sails of the opposition and sent clear warnings to Merkel eight months ahead of the federal vote, after three years of setbacks in state elections for the CDU.
Merkel needs the FDP at national level to haul themselves over the 5 percent threshold to continue her coalition.
"The CDU has now seen very clearly how bad things can go when you campaign for a split vote, as it did for the benefit of the FDP," said Oskar Niedermayer, political scientist Berlin Free University.
Although McAllister denies any vote-sharing strategy, he repeated throughout the campaign that he wanted to continue to govern with the FDP and even attended one of their rallies.
"People voted strategically at the last moment. The FDP got votes based on the fear that McAllister wouldn't get back in power. But in the end too many people thought like this," said Richard Hilmer, head of pollster Infratest dimap.
"Germany's voting system, which allows people two votes, encourages people to try and craft the coalition they would like to see, but the danger is that this can have incalculable results," he told Reuters.
Merkel, appearing alongside the crestfallen McAllister on Monday, stressed the CDU would campaign solely for itself in the national election: "One of the lessons from Lower Saxony is that we don't need to be so afraid that the FDP will vanish from the picture ... It is important that we don't target the same votes."
The Lower Saxony election offers lessons for Merkel not just on coalition arithmetic and vote sharing but also on the risks of relying too heavily on personal popularity.
McAllister, the 42-year old son of a British soldier and a German mother was by far the most popular candidate, not least because of his colourful election campaign, dismissed by the opposition as a "Cuban-style personality cult". He played up his Scottish roots, complete with bagpipes for his campaign music.
Yet it was the more sober, less personality-driven campaigns of the SPD and Greens that won support in Lower Saxony, where voters remember all too well the demise of their notoriously flashy previous state premier, Christian Wulff from the CDU.
Handpicked as German president by Merkel, Wulff was forced to resign in disgrace last year over his personal finances.
Merkel herself has a huge advantage over SPD challenger Peer Steinbrueck. A poll last week gave her 59 percent of the vote compared with just 18 percent for Steinbrueck, but pollsters see support for her centre-right coalition waning.
"The centre-right government itself is not that popular. Economically they have been successful, but at the expense of policies of social equality. This is much more on voters' minds now, particularly when times are tougher," said Hilmer.
Although the SPD jeered that the FDP owed its survival in Lower Saxony to a "blood transfusion" from the CDU, the liberal party's leader Philipp Roesler won a reprieve after criticisms that he had let it slide in nationwide polls to just 2 percent.
But in a sign of lingering unhappiness with Roesler, the FDP put veteran parliamentary leader Rainer Bruederle in charge of the campaign for September's federal elections.