5.1 Representation of mode choice and its causes
The model simulates changes in three modes and three trip purposes or a 3 × 3 grid of purpose-mode combinations. The transport modes are car, public transport and active travel. Active travel includes walking and cycling. The mode categories serve as both targets of policies and emission impact categories. The trip purposes are commutes, errands, and leisure. Different trip types have different potential for being travelled by a given mode, informed by starting state data and assumptions. Policies and other urban change can also target different trip types. A road toll may for instance only apply during typical commuting hours or desired leisure activities can change.
Mode choice is affected by four endogenous causes: crowding, trends, safety in numbers and affect. Additionally, exogenous causes were included: cost, capacity (higher capacity alleviates crowding), and feasibility. Feasibility sets a maximum use of a mode for a given purpose. Since we calculate mode share from feasible trips, increasing mode feasibility also increases mode use (mode use divided by feasible trips by the mode is constant while feasible trips increase), though we do not present that scenario in this paper. Excluding feasibility, the other causes of mode use are calculated in terms of relative change since start. The degrees of their effect are governed by weight parameters, and all weighted effects are multiplied to produce a relative change in mode shares (see Sect. 6 for discussion, and Section 1.1 of the Additional file 1 for the mathematical formulation).
One limitation is that the multiplicative form of calculating mode share could be contested. Another is that the model has no mechanism for calculating movement between specific modes: which of the two other modes are given up when one mode grows, and which mode is abandoned when one declines. Such changes need to be assumed. We make optimistic assumptions from an emissions impact perspective (see Section 1.4 of the Additional file 1).
5.2 Postulated feedback loops
Our selection of feedbacks is not intended as a default theory of mode choice dynamics, but as a demonstration of the principle that policy effects depend strongly on the assumed system and that a small dynamic model can allow meaningful comparison between different policies and theories of change. Here we narratively explain each dynamic. We also briefly explain their operationalization in the model. Each feedback is assigned a weight parameter governing its strength of effect (if any). We use parameter values with diminishing marginal effect to prevent uncontrolled exponential growth also under narratively reinforcing effects (see Section 1.2 of the Additional file 1). Figure 1 illustrates our feedback loops. In the Figure, R and B refer to reinforcing and balancing loops and crossed lines indicate delayed effect.
Crowding (balancing loop): When more travellers opt for public transport or car travel, those modes (vehicles, roads etc.) become more crowded [2, 20, 33]. Crowding can manifest, for instance, as a loss of comfort or as concern over late arrivals. Inversely, when fewer people travel with these modes, they appear more attractive. In the model, crowding effects can be alleviated by expanding capacity. If mode use increased by 10% while capacity increased by the same amount, there would be no net crowding effect.
Safety in numbers (reinforcing loop): If the number of accidents increases less than proportionally to the volume of traffic (e.g. if traffic doubles, the number is less than doubled), a safety-in-numbers effect may be in play [9]. A motorist is less likely to collide with a person walking and bicycling if more people walk or cycle [29]. Thus, a larger number of active travellers makes active travel feel safer and encourages more active travel. In the model, a higher number of cyclists relative to start increases the safety-in-numbers effect, encouraging more cycling. Infrastructure capacity is not included as a variable for cyclists and safety in numbers does not apply to public transport and car travel.
Trends (reinforcing and balancing loops): This dynamic may represent excitement around a new travel opportunity, wanting to fit in, and being curious about current developments such as car-free lifestyles. Such a social contagion effect is typical in system dynamics models (e.g. [6]). In our model, mode popularity is affected by “recent change” in its popularity, or current mode use minus a lagged value of mode use. When the rate of increase/decrease in mode use starts slowing down, so does the reinforcing feedback, resulting in a combination of reinforcing and balancing effects.
Affect (reinforcing loop): Changes in affect or an underlying societal attitude regarding normal and desirable behaviour can drive social change [45]. However, it is also challenging to conceptualize in way that allows using ‘(relative) changes in affect’ as a numeric input to mode choice. In the model, our solution is to understand affect as stemming from mode choice change since start. When more/fewer trips are taken with a mode, the affect effect of that mode increases/decreases. It is mathematically distinct of the safety-in-numbers effect by being formulated based on mode split per trip purpose, while the safety-in-numbers effect is based on the absolute number of active travel trips per trip purpose.
5.3 Dynamics of the model
Before the impact assessment demonstration using the full model, we show the dynamics that follow each endogenous factor. In the following tests, the same exogenous improvement was implemented while activating different feedbacks. We use the same weight parameter value for each feedback. The key here is to qualitatively compare the shapes of the curves rather than scrutinize alternative test settings or observe the exact y-axis value. In Section 4 of the Additional file 1, we show that results of this qualitative comparison of dynamics do not change with alternative parameter values, though naturally the numeric degree of change is affected.
Crowding: Figure 2 demonstrates the crowding dynamic. Since crowding is a balancing feedback loop, it reduces change caused by interventions (other than capacity interventions which alleviate the crowding effect). A symmetrical effect for car travel would be that when car travel is discouraged, car travel becomes less crowded which to some extent undermines the discouragement of car travel. The weight of the crowding effect also determines the effectiveness of capacity increases/decreases to encourage/discourage travel.
Safety in numbers: The solid orange curve in Fig. 3 demonstrates the safety-in-numbers dynamic. A safety-in-numbers effect for active travel increases the impact of interventions. Whatever positive effect is put in motion gets accelerated and reaches a higher outcome.
Trends: The dashed black curve in Fig. 3 demonstrates the trends dynamic. The more weight is given to trends, the larger is the oscillation effect. When growth slows down, the trend effect declines. Since part of prior growth was due to the trend effect, growth slows down even more, eventually causing a negative trend effect. Mode decline also slows down eventually, reducing the negative trend effect, and thus the oscillation turns to an upswing.
Affect: The dashed orange curve in Fig. 3 demonstrates the affect dynamic. Affect works similarly to the safety-in-numbers effect: prior change in mode choice is amplified. However, note that the trajectories under the affect assumption and the safety-in-numbers assumption differ despite using the same weight parameters. This shows the significance of different mathematical formulations for feedback loops that narratively emerge from the same phenomenon (in this case mode choice).
Figure 4 demonstrates how alternative combinations of endogenous effects can lead to very different outcomes. All four curves in Fig. 4 feature the same intervention to make active travel easier. All activated feedback loops use the same weight parameter. The solid orange curve and solid black curve apply the trend and affect dynamics respectively. The dashed orange curve activates both effects at once. The trend and affect effects support one another: trends build up the mass of behavioural change, which generates affect, while increasing affect maintains the growth of active travel to mitigate the downward cycle of the trend oscillation effect. Growth is faster compared to the solid black curve, and an equal or higher level of active travel is achieved at all times compared to the solid orange curve.
However, combining endogenous causalities can also lead to strange and adverse effects. The dashed black curve in Fig. 4 shows active travel dipping below the starting values for a moment despite a positive intervention. This result followed combining the trend effect with the safety-in-numbers effect. Safety in numbers amplifies the oscillation effect of trends by quickly removing/increasing support of active travel when the trend effect goes into a downturn/upturn.
We draw three conclusions from the combined dynamics demonstrations. First, narratively simple changes to causal assumptions can lead to qualitatively different trajectories of change that can also imply highly divergent numeric outcomes. Second, explaining or targeting rapid and large-scale behavioural change benefits from (correctly) identifying dynamics that could compound positive effects and mitigate unwanted effects. Third, constructing alternative theories of change as feedback structures for simulations allows scrutinizing and refining them. For instance, if we were to think that both trend effects and safety-in-numbers effects are key factors of transition, then we also need an explanation for why the wild oscillation of the dashed black curve in Fig. 4 would not/does not occur.
5.4 Impact assessment demonstration: emission reductions from policies directed at mode choice in Helsinki
In this section, all causal factors are used to demonstrate how the impact potential of interventions may be analysed when feedback structures are defined but many parameters of the system are highly uncertain. Discussion of our minimum and maximum weights is in Section 1.3 of the Additional file 1, and intervention descriptions in Section 2 of the Additional file 1. The principles of analysis can be understood in isolation of these precise test settings.
Figure 5 shows four emission scenarios for the same set of interventions but alternative assumptions of the strength of the initial exogenous interventions and subsequent endogenous dynamics. The exogenous interventions are cost increases of car use, cost decreases of public transport use, ease increase to active travel and public transport, and capacity increase for public transport. The dashed orange curve uses maximum weights for exogenous and endogenous effects. The dashed black curve uses minimum weights. The large difference between the two curves indicates that emission effects are highly sensitive to the combined weightings of feedback effects.
Between the two extremes in Fig. 5 are intermediate cases. In these cases, weights are grouped as (arguably) social phenomena that are reactions to the behaviour of others—trends and affect—and (arguably) more individualistic reasoning—costs, ease, and comfort (crowding and safety in numbers) of travel. When the weights of ‘individualistic’ factors are set to maximum and social causes to minimum (solid black curve), emissions decline more than in the inverse case (solid orange curve). One explanation is that there are a larger number of effects in the ‘individualistic’ category. Another would be that the ‘individualistic reasoning’ effects produce the initial behavioural change upon which ‘social’ reactions continue to expand—whatever the weighting of the latter.
Figure 6 makes the same set of interventions but samples all weights randomly between the minimum and maximum (using Latin hypercube sampling over 200 repetitions). The method assumes that all parameter values within their respective ranges are equally likely. The 50% band of results (orange shaded area) is closer to the most pessimistic than the most optimistic outcomes, meaning that the most optimistic results rely on a rather specific set of weight conditions. Observing outcomes for individual modes revealed that active travel featured clearly the highest variance in results including particularly strong best optimistic results. If the model were accepted as a starting point, analysis could thus progress to investigate how the causes of active travel could be targeted specifically (in the real world) to promote achieving the best outcomes under uncertainty.
Another takeaway is that the set of intervention did not lead to undesirable outcomes such as increasing emissions or declining active travel under any combination of parameters, even though we showed this to be possible in principle under combined nonlinear dynamics (Fig. 4). The lowest emission reduction in the model for this set of interventions was around 10%.
Finally, it is possible to compare alternative policy approaches under parameter uncertainty. Using the same sampling as in the previous test, Fig. 7 shows the results for an improvement in ease to active travel and public transport. Figure 8 shows the results for cost increases to car travel and cost reductions to public transport. The ease increases led to somewhat better results in the 50% band and the most optimistic runs than the cost interventions. It is also notable that combining multiple interventions in the context of uncertainty (Fig. 6) avoided the worst possible outcomes shown in Figs. 7 and 8 while securing a better 50% band.