How to design ballot papers with a large number of candidates in a preferential system? Background: In the 2013 Australian Federal election, several parties were elected to the senate seemingly because of usability issues related to the ballot paper (see here for discussion). For example: 


  [The] Australian Sports Party has no policies other than advocating lots
  of sport, and won just 0.22 per cent of the vote. But with preferences
  from other small parties, they are likely to get a Senate quota ahead of
  the second Labor candidate, who had 12.33 per cent.


For those unfamiliar with the Australian federal electoral system, the Senate is the upper house. Each state has an equal number of senators. Election to the senate requires that you achieve a certain percentage of votes in a given state. It is a preferential block voting system. Thus, you can achieve the required votes after preferences have been allocated.

On the current ballot, you can either vote above the line or below the line. Above the line involves ticking a single box and accepting the allocation of preferences of that particular party. Ticking below the line requires that you number every candidate from one to the number of candidates (which could be over 100). Thus, the according to wikipedia about 98% of people vote above the line.

A strange situation arose in the 2013 election where several micro-parties appear to have won senate seats due to a flaw in the combination of the preferential and the above the line system. This seems to have been brought on by a range of factors including a general across the board increase in the vote for micro-parties and collaboration in micro-parties in allocating preferences to each other.  Traditionally, when the likely senator was one of only a few parties, the allocation of preferences was fairly clear. However, many voters if explicitly asked about their preferences, may have put one of the major parties above some of the more obscure parties that seem to have been elected based on preferences.

Thus, there is a problem:


There are too many candidates to make it easy for people to indicate their preferences for all candidates.
The preferences implied by putting a 1 in a box "above the line" (i.e., accepting the preferences of a given party) may often not be consistent with what a voter would intend their preferences to be were they asked to think about it.


Questions


What is a good way to design ballot papers with a large number of candidates in a preferential system so that it is easy to use and conveys the important aspects of people's preferences?
What psychological theory or empirical research justifies such a ballot paper?
This is a partial answer to your question, there is considerable research touching on specific designs and strategies in ballots that will be outlined below

This issue has come up in research around the world.  A specific concern is:


  Ballot design can be an important factor in determining whether voters are able to cast a ballot accurately, which can influence the legitimacy of elections.


Source: "Ballot design and Unrecorded votes on paper-based ballots" (Krimball and Kropf, 2005).

Krimball and Kropf assert that there is a lot in common between a ballot and a self-administered questionnaire, in that voters must process a myriad of verbal, symbolic and graphical language (which includes the written instructions etc).  There has been some research in making ballot papers more 'realistic' so to speak.

Research in Britain has looked into including a photo with the ballot, according to "Candidate appearance and voting in British elections: The potential impact of ballot paper photographs" (Johns, 2008), asides from making an Australian Senate ballot sheet the size of Tasmania:


  Some MPs express worries that voters may be swayed in their choice by the photos. This concern is consistent with psychologists’ findings that we automatically make judgements about people’s characters based on the briefest inspection of facial appearance, and that these judgements influence behaviour towards them. This is especially true when, as with most constituency candidates, we know little else about the people. 


Swinburne Politics Professor Brian Costar, in the online article "We need to simplify voting for the Senate" suggests:


  the Senate ballot paper should be redesigned to abolish above- and below-the-line voting. Instead, voting should be optional preferential. At a normal Senate election, a voter would need to number at least six squares, and at a double dissolution election at least twelve. This would keep informal voting low and put a stop to secret wheeling and dealing over preferences and unexpected successes for candidates with extremely modest direct support.


One main problem is, according to the empirical analysis "Influence of ‘Cognitive Sophistication’ on Ballot
Layout Effects" (Geys and Hayndels, 2003), is that


  Candidates in ‘critical’ (top and
  bottom) positions in multi-column ballots obtain a larger percentage of the vote in
  multi-column ballots than in a single-column ballot.


These positions are, according to the authors, in the top and bottom corners.  But, the authors assert that this is actually not a huge issue, given


  The results of our empirical analysis have shown that cognitive sophistication
  of the electorate does have a strong effect. A larger share of highly
  educated (or richer) voters significantly reduces the strength of Ballot Layout
  Effects.


However, a key point from the article is that


  avoiding layout effects by randomizing the order of candidates or using
  additional layouts such that each politician has an equal probability of being
  on top (bottom) of a column may be hard to use in practice.


An interesting point the authors found in regards to computerised ballots is that


  preferential votes are more evenly
  distributed among candidates when voting is done via computerized ballots.


Further information could be sourced from the International Centre for
Electoral Psychology

Anecdotal side note: In my electorate (I am an Australian also), we had the same thing happen - about 30 above the line, and over 100 below the line for the Senate.  I have wondered about this also - I am "apolitical" (this is not up for discussion) and could not be bothered doing the 'under the line' thing - this apathy was a topic of conversation when I was in the long queue to get into vote (Reminder to everyone else, voting is compulsory in Australia).

The point of this anecdote is that voter enthusiasm (or lack thereof) could also be a factor in the effectiveness of any ballot design.