AKB48 Group is the world’s largest girls idol group based in Tokyo, Japan. It contains six smaller constituent groups called sister groups with over 300 members in total. Naturally the popularity of each member is different which should follow a relatively symmetric unimodal distribution. Since there is no way every member can get equal and adequate opportunities to perform, a dozen or so prominent members are selected to receive half of the attention. As the histogram below shows, however, the popularity distribution (measured by number of followers on Showroom) is very right skewed due to at least two effects: (1) the distribution of media exposure is extremely right skewed and (2) the number of years since joining the group is right skewed. We know that media exposure can shape member popularity by contrasting the popularity distribution to that of a more egalitarian group named Keyakizaka46, which has very symmetric and concentrated popularity distribution and media exposure distribution. Keyakizaka46 is able to achieve relative equality of media exposure due to its small size of 21 members (not counting under group members).
In every single by AKB48, 16-32 members are selected to perform for the main song and about 60 more perform in the coupling songs. We can think of the selection of members in each single as an exploitation-exploration problem where each member has a popularity function that has age, cumulative media exposure, and potential maximum popularity as parameters. We can reasonably assume that popularity is an increasing and concave function of cumulative media exposure that asymptotically achieves the potential maximum popularity, and popularity increases and then decreases with age (holding everything else constant).
The goal of the management is to assign an amount of media exposure to each member in each single in order to maximize total popularity summed over each member and across all singles (ignoring financial discounting by assuming sustainability is also their goal). They can exploit by keep selecting the current most popular members, or they can explore by selecting less popular members and see how their popularity grows. In addition, the fan base of AKB48 can change in size which acts like a multiplier for the internal popularity described above. The overall weighted quality of all members affects how the fan base changes.
The Decline of AKB48
AKB48 reached its peak in 2013 and has lost about three quarters of its popularity since then. Every aspect of AKB48, including songs and quality of members, is said to have deteriorated except the group’s size. With twice the size than 2013 and ever more young girls auditioning for AKB48, it’s very unlikely that the quality of members has dropped. The decline should be mostly attributed to having too much exploitation and too little exploration. That is, the management relied too much on senior prominent members and gave new members too little opportunity as we will see in their general elections and the changes in rock-paper-scissors tournament.
As an extreme case of exploitation, the center (the most starred member) of many singles, especially recent ones, are graduating prominent members. It is a way to show respect to these graduating members but this promotion has zero positive externality for future singles and is unfriendly for future fans who are not interested in graduated members. In addition, prominent members get a special graduation song in their last single. This graduation song is often the “B-side song” which gets more attention than other coupling songs in the single and is included in all five types of the single.
Currently, when a promising junior is finally selected for a single, she is usually half way in her career and there is much less time and youth for her to grow to become a prominent member like her predecessors who dominated AKB48 in 2010-2014. By using more junior members as the center instead, AKB48 would suffer slightly in the sales but future sales would increase due to increased popularity of the new center, thus benefiting from exploration.
The general elections (or Senbatsu Sousenkyo) are annual elections that determine the members and positions for AKB48’s next single voted by the fans who buy their previous single and online subscription members. One fan is by far not limited to having one ballot. Selecting 16-32 members out of 300+ for each single is a very difficult task since popularity and its underlying popularity function for newer members are hidden. The general election is a brilliant way for the management to estimate the current popularity of each member while making the fans feel more democratic, and so even in singles that are not binded to general elections (3/4 of all singles), the selection of members is somewhat affected by the most recent general election results.
The general elections come with some serious drawbacks. If a member’s vote count is not in the top 80, the votes are wasted and she does not receive any ranking. So fans of rising members who have never ranked have to coordinate and predict whether they will spend the money and push her into top 80 this time. This uncertainty of not knowing whether the vote will be wasted could discourage voting although it’s alleviated by a mid-report that publishes the tentative top 100 members.
Unfortunately, the mid-report might even worsen the accuracy of the general election for estimating the popularity of members. The mid-report takes place when only 5% of the voting period is past and 1/3 of the votes are casted. Typically before the mid-report, a small number of fans cast a lot of votes for their favorite member, hoping to push her into the top 100 by the mid-report. If they succeed, they signal the other fans who have not voted that this member will likely rank this time and therefore they should vote more. Since whether a member who has never ranked will enter top 80 is dependent on this small group of fans who vote before the mid-report, it’s less accurate for the election results to estimate current popularity.
The general election is almost purely an exploitative method since it samples the current distribution of popularity and projects it to the next single. If fans are not biased to voting for new and upcoming members, they will unlikely gain fame through general elections. The uncertainty of wasting a vote also make the general elections even more exploitative by increasing the barrier to rank for the first time. Interestingly, the randomness that the mid-report adds to the final outcome can be considered a small scale blind exploration, regardless of whether it’s the initial purpose of the mid-report.
To make every vote count, the management could refund wasted votes or at least publish the ranking for every member. But a more realistic approach is to allow for multiple candidates on each ballot in order specified by the voter. The first candidate of each ballot is counted. If the first candidate does not rank in the top 80, the second candidate on these ballots are counted. This can repeat if the second candidate is also not ranked. This method assumes that every voter has a fixed budget that they want to use to vote for their favorite member who will rank which is not very true, but this method is a compromise between certainty and simplicity.
To promote rising members as a way to increase exploration, one simple change is to add a B-side song consisting of members whose number of votes increased the most and those who rank for the first time.
Another annual event of AKB48 is the rock-paper-scissors tournament (or Janken Taikai). All members are paired to play rock-paper-scissor and typically the final 7 members (formerly 16) are selected for the next single. This tournament used to be as important as the general election in 2010-2013 when it was used to determine the members for the next single. Since 2014, the top members of the tournament only get to release a separate “debut” single at less budget and with fewer coupling songs, which sales only 1% of that of their main singles. This change is probably due to the fear that members randomly selected from the tournament would end their long streak of singles selling over a million copies. This is because (1) the average sale has already decreased from around 1.5 million to slightly over 1 million and (2) when the group grows in size, the proportion of members that are lesser known is significantly higher and thus further harming the sale. In fact, the management has used many tactics to support the sales volume to hide the decreasing popularity of AKB48.
The rock-paper-scissors tournament is purely explorative in that every member has an equal chance of winning. Simply put, The risk of being too explorative forces this event to be less influential and not binded to the next single. As we said, the general election is too exploitative and the rock-paper-scissors tournament is too explorative.
A great alternative is to revise the rules of the rock-paper-scissors tournament by combining the two and bind the results to the next single just like before 2013. First, let the fans vote for all members just like that in the general election. Then categorize the members by the number of votes they receive on a logarithmic scale. The members who cast over 1/64 of all votes are automatically in the top 64 and only need to win two rounds to be in the top 16 (selected for the next single). The members who receive between 1/64 and 1/128 of the votes are in the top 128 and need to win one more round to achieve the same outcome. This goes on for all members. As shown below, the purple members have twice the chance of the blue member and four times the chance of the green members to be the final winner.
This new method is similar to probability proportional to size sampling where the size is popularity and the sample is members for the next single. It balances among exploitation, exploration, simplicity, and the excitement of a tournament. On average, half of the winning members will be from the top 79 most popular members and a quarter will be from the top 26 most popular members.
In the general election, the distribution of the number of votes casted by a fan is extremely skewed. Often over 5% of the votes for a member come from one fan who buy over 1000 ballots. Sometimes it’s informative to weigh each fan equally since the number of fans indicates potential growth and social influence which matter a lot in the long run. The down side is of course a loss of income by forbidding the purchase of multiple votes. To balance this, either the general election or the rock-paper-scissors tournament can be chosen to implement this no duplicated votes policy. This was actually done once in 2016 for the 67th Kohaku Uta Gassen and the outcome was very different from that year’s general election.
Mixing Members from Different Sister Groups
From the fan’s point of view, pursuing AKB48 is also an exploitation-exploration problem. They need to balance between following their current favorite members and meeting new members. The management should facilitate this process by better structuring the group and wisely distribute the resources and opportunities among members. AKB48 Group consists of six sister groups; each sister group usually consists of three teams, each with around 16 members. This hierarchical structure guides new fans by giving them a natural order. Fans typically start by following one member, and then her team, and then her sister group. There used to be many sub-units consisting of 3 to 7 members each releasing their own singles; these units served as a more detailed guide in introducing members to new fans by categorizing the members and giving each member a unique characteristic.
This hierarchical structure has become more and more irrelevant as the sister groups often mix together in most events including songs, the rock-paper-scissors tournament, concerts, song festivals, and TV shows. The members are constantly shuffled and it’s very difficult to often see the same three-people unit on stage. Some mixing is necessary to introduce senior fans to more sister groups and members, but new fans can get overwhelmed by this as they are not ready to do that much exploration at first. Currently there are three less active sub-units but the members share little common characteristics and are from mixed teams and sister groups which breaks the hierarchical structure.
Distribution of Resources
It’s impossible to find out the best distribution of resources and opportunities without experimenting. Certainly for a group of this size, a lot of resources should be concentrated to a few members in a power-law distribution fashion. The benefit is that new fans who are capable of getting to know only a few to a dozen members will have the opportunity to do so. One way to discover the optimal distribution faster is to experiment with different distribution within each sister group and compare the results. Similarly, the management could experiment in sister groups first when they face any difficult decision.